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Deck 4: Applications of the Derivative
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Question
Given the graph of 
, locate the absolute extrema (if they exist) on the interval 
. 
A) absolute max:
B) absolute min:
C) absolute min:
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max:
B) absolute min:
C) absolute min:
D) no absolute extrema
Question
Using Newton's method with 
, determine the third iteration when approximating the root to at least six-digit accuracy of the following equation. x3 + x2 - 5x + 4 = 0
A) -3.062500
B) -3.060647
C) -3.060691
D) -3.060992
, determine the third iteration when approximating the root to at least six-digit accuracy of the following equation. x3 + x2 - 5x + 4 = 0A) -3.062500
B) -3.060647
C) -3.060691
D) -3.060992
Question
Find the linear approximation, L(x), to f(x) at x = x0. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Given the graph of 
, locate the absolute extrema (if they exist) on the interval 
. 
A) absolute max:
B) absolute min:
and 
C) absolute min:
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max:
B) absolute min:
and C) absolute min:
D) no absolute extrema
Question
Given the graph of 
, locate the absolute extrema (if they exist) on the interval 
. 
A) absolute max:
B) absolute min:
and 
C) absolute min:
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max:
B) absolute min:
and C) absolute min:
D) no absolute extrema
Question
Find the linear approximation at x = 0 to show that the following commonly used approximation is valid for "small" x. 
Question
Use linear approximation of 
at 
to estimate the quantity of 
to the nearest ten thousandth.
A)
B)
C)
D)
at to estimate the quantity of to the nearest ten thousandth.A)
B)
C)
D)
Question
Use a linear approximation to estimate 
A) 0
B) 0.18
C) 0.1
D) 0.02
A) 0
B) 0.18
C) 0.1
D) 0.02
Question
Use a linear approximation to estimate 
Note that 17.2 is near 16 which is 
A) 3.23649
B) 2.03649
C) 2.0375
D) 3.08312
Note that 17.2 is near 16 which is A) 3.23649
B) 2.03649
C) 2.0375
D) 3.08312
Question
Question
A certain company estimates that it can sell f(x)-thousand video game consoles at the price of $x as given in the table. 
Use a linear approximation to estimate the number of consoles that can be sold at $62.
A) approximately 105 thousand consoles
B) approximately 108 thousand consoles
C) approximately 130 thousand consoles
D) approximately 138 thousand consoles
Use a linear approximation to estimate the number of consoles that can be sold at $62.A) approximately 105 thousand consoles
B) approximately 108 thousand consoles
C) approximately 130 thousand consoles
D) approximately 138 thousand consoles
Question
Find the linear approximation at x = 0 for each of f (x) = (x + 1)2 + 5, g(x) = 6 + sin(2x) and 
. Graph each function together with its linear approximation.
. Graph each function together with its linear approximation. Question
Use Newton's method to find an approximate root of the equation 
(accurate to six decimal places).
A) 0.306232
B) 0.216232
C) 0.136232
D) 0.219565
(accurate to six decimal places).A) 0.306232
B) 0.216232
C) 0.136232
D) 0.219565
Question
-The impedance Z of a simple RL (resistive inductive) circuit is given by
, where R is the resistance of the resistor, L is the inductance of the inductor, and is the angular frequency of the applied voltage. Find a linear approximation of Z(L) for small values of L assuming all other quantities are constant. Show all of your work. Question
Find the linear approximation, L(x), to f(x) at x = x0. 
A)
B)
C)
D)
A)
B)
C)
D)
Question
Approximate 
accurate to 3 decimal places using Newton's method. State the function used.
A) 2.289 using
B) 2.359 using
C) 2.219 using
D) 2.289 using
accurate to 3 decimal places using Newton's method. State the function used.A) 2.289 using
B) 2.359 using
C) 2.219 using
D) 2.289 using
Question
Explain why Newton's method fails for the following equation with the specified initial guess. 
A) Using
we see that f is not differentiable at 
B) Using
we obtain 
.
C) Using
we obtain 
which will give 
D) Using
we see that f does not have any real roots.
A) Using
we see that f is not differentiable at B) Using
we obtain .C) Using
we obtain which will give D) Using
we see that f does not have any real roots. Question
Newton's method fails for the given initial guess. Explain why the method fails and, if possible, find a root by correcting the problem. Round to four decimal places, if necessary. 
, x0 = -1
A) f '(-1) = 0; -1.905, 0.105
B) f '(-1) does not exist; -1.905, 0.105
C) f (-1) = 0; 1.905, -0.105
D) f (-1) does not exist; 1.905, -0.105
, x0 = -1A) f '(-1) = 0; -1.905, 0.105
B) f '(-1) does not exist; -1.905, 0.105
C) f (-1) = 0; 1.905, -0.105
D) f (-1) does not exist; 1.905, -0.105
Question
Given the graph of f(x), draw in the tangent lines used in Newton's method to determine x1 and x2 after starting at x0 = 1. 
Question
Question
Given the graph of 
, locate the absolute extrema (if they exist) on the interval 
. 
A) absolute max:
absolute min: 
B) absolute max:
absolute min: 
C) absolute max:
absolute min: 
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max:
absolute min: B) absolute max:
absolute min: C) absolute max:
absolute min: D) no absolute extrema
Question
Given 
determine if the critical number 
represents a local maximum, local minimum or neither.
A) local maximum
B) local minimum
C) neither
determine if the critical number represents a local maximum, local minimum or neither.A) local maximum
B) local minimum
C) neither
Question
Given 
determine if the critical number 
represents a local maximum, local minimum or neither.
A) local maximum
B) local minimum
C) neither
determine if the critical number represents a local maximum, local minimum or neither.A) local maximum
B) local minimum
C) neither
Question
Find the absolute extrema of the given function on the indicated interval. 
on 
A) absolute maxima:
, absolute minimum: 
B) absolute maximum:
, absolute minimum: 
C) absolute maximum:
, absolute minimum: 
D) absolute maximum:
, absolute minimum: 
on A) absolute maxima:
, absolute minimum: B) absolute maximum:
, absolute minimum: C) absolute maximum:
, absolute minimum: D) absolute maximum:
, absolute minimum: Question
Given the graph of 
, locate the absolute extrema (if they exist) on the interval 
. 
A) absolute max:
absolute min: 
B) absolute min:
C) absolute max:
absolute min: 
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max:
absolute min: B) absolute min:
C) absolute max:
absolute min: D) no absolute extrema
Question
Given 
, determine the critical number(s).
A)
B)
C)
D)
, determine the critical number(s).A)
B)
C)
D)
Question
Given 
, determine the absolute extrema on the interval 
.
A) absolute max:
; absolute min: 
B) absolute max:
and 
; absolute min: 
and 
C) absolute max:
; absolute min: 
D) absolute max:
; absolute min: 
, determine the absolute extrema on the interval .A) absolute max:
; absolute min: B) absolute max:
and ; absolute min: and C) absolute max:
; absolute min: D) absolute max:
; absolute min: Question
Given 
, on the interval 
, determine if the critical number 
represents a local maximum, local minimum or neither.
A) local maximum
B) local minimum
C) neither
, on the interval , determine if the critical number represents a local maximum, local minimum or neither.A) local maximum
B) local minimum
C) neither
Question
Given 
determine the critical number(s).
A)
B)
C)
D)
determine the critical number(s).A)
B)
C)
D)
Question
Given the graph of 
, locate the absolute extrema (if they exist) on the interval 
. 
A) absolute max: approximately
absolute min: 
B) absolute max:
absolute min: 
C) absolute max:
absolute min: 
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max: approximately
absolute min: B) absolute max:
absolute min: C) absolute max:
absolute min: D) no absolute extrema
Question
Find all critical numbers. 
A)
B)
, 
C)
D)
A)
B)
, C)
D)
Question
Given the graph of 
, locate the absolute extrema (if they exist) on the interval 
. 
A) absolute max: approximately
B) absolute max: approximately
absolute min: 
C) absolute max: approximately
absolute min: 
Absolute min:
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max: approximately
B) absolute max: approximately
absolute min: C) absolute max: approximately
absolute min: Absolute min:
D) no absolute extrema
Question
Determine all critical numbers of 
.
A)
B)
C)
D)
.A)
B)
C)
D)
Question
Find all critical numbers. Then use a graph to determine whether the critical numbers represent a local maximum, local minimum, or neither. 
A)
(local maximum), 
(neither), 
(local minimum)
B)
(local maximum), 
(local maximum), 
(local minimum)
C)
(local maximum), 
(local minimum)
D)
(local minimum), 
(local maximum)
A)
(local maximum), (neither), (local minimum)B)
(local maximum), (local maximum), (local minimum)C)
(local maximum), (local minimum)D)
(local minimum), (local maximum) Question
Given the graph of 
, locate the absolute extrema (if they exist) on the interval 
. 
A) absolute max:
absolute min: 
B) absolute min:
C) absolute max:
absolute min: 
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max:
absolute min: B) absolute min:
C) absolute max:
absolute min: D) no absolute extrema
Question
Find the absolute extrema of the given function on the indicated interval. 
on 
A) absolute maximum:
, absolute minimum: 
B) absolute maximum:
, absolute minimum: 
C) absolute maximum:
, absolute minimum: 
D) absolute maximum:
, absolute minimum: 
on A) absolute maximum:
, absolute minimum: B) absolute maximum:
, absolute minimum: C) absolute maximum:
, absolute minimum: D) absolute maximum:
, absolute minimum: Question
Given the graph of 
, locate the absolute extrema (if they exist) on the interval 
. 
A) absolute max: approximately
B) absolute max:
absolute min: 
C) absolute max:
absolute min: 
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max: approximately
B) absolute max:
absolute min: C) absolute max:
absolute min: D) no absolute extrema
Question
Determine all critical numbers of 
.
A)
B)
C)
D)
.A)
B)
C)
D)
Question
Given 
, on the interval 
, determine the critical number(s).
A)
B)
C)
D)
, on the interval , determine the critical number(s).A)
B)
C)
D)
Question
Question
Find the intervals where the function is increasing and decreasing on the specified interval. Use this information to determine all local extrema. 
on 
on Question
Determine the intervals where 
is concave up and concave down.
A) concave down for
concave up for 
B) concave down for
concave up for 
C) concave down for
cancave up for 
D) concave down for
and 
concave up for 
is concave up and concave down.A) concave down for
concave up for B) concave down for
concave up for C) concave down for
cancave up for D) concave down for
and concave up for Question
Using a calculator or computer, estimate the absolute extrema of 
on the interval 
. Round answer to the nearest hundredth.
A) absolute max:
; absolute min: 
B) absolute max:
; absolute min: 
C) absolute max:
; absolute min: 
D) absolute max:
; absolute min: 
on the interval . Round answer to the nearest hundredth.A) absolute max:
; absolute min: B) absolute max:
; absolute min: C) absolute max:
; absolute min: D) absolute max:
; absolute min: Question
Find all asymptotes and extrema and sketch a graph. 
Question
Determine, by hand, all critical numbers of 
and use the First Derivative Test to classify each as a local minimum, local maximum or neither.
A) local maximum at
local minimum at 
Neither:
B) local maximum at
local minimum at 
Neither:
C) local maximum at
local minimum at 
Neither:
D) local maximum at
local minimum at 
Neither:
and use the First Derivative Test to classify each as a local minimum, local maximum or neither.A) local maximum at
local minimum at Neither:
B) local maximum at
local minimum at Neither:
C) local maximum at
local minimum at Neither:
D) local maximum at
local minimum at Neither:
Question
Find all asymptotes and extrema and sketch a graph. 
Question
A herd of ninety-nine antelope is released onto a small game reserve so that their reproductive habits can be studied. In the beginning the population of the herd increases rapidly in size but eventually slows due to a dwindling food supply. Suppose the population of antelope after t years is given by the function 
where 
. Determine when the population begins to decline.
A) 15 years
B) 17 years
C) 18 years
D) 19 years
where . Determine when the population begins to decline.A) 15 years
B) 17 years
C) 18 years
D) 19 years
Question
Find the x-coordinates of all extrema and sketch the graph showing global and local behavior of the function. Round answers to nearest thousandth. y = x5 - 150x3 + 460x + 9
A) local max: x = -1.017, x = 9.432 local min: x = -9.432, x = 1.017
B) local max: x = -9.432, x = 1.017 local min: x = -1.017, x = 9.432
C) local max: x = -1.0343 local min: x = 1.0343
D) local max: x = 1.0343 local min: x = -1.0343
A) local max: x = -1.017, x = 9.432 local min: x = -9.432, x = 1.017
B) local max: x = -9.432, x = 1.017 local min: x = -1.017, x = 9.432
C) local max: x = -1.0343 local min: x = 1.0343
D) local max: x = 1.0343 local min: x = -1.0343
Question
Determine, by hand, the interval(s) where 
is increasing and/or decreasing.
A)
B) increasing
; decreasing 
C) increasing
; decreasing 
D) increasing
; decreasing 
is increasing and/or decreasing.A)
B) increasing
; decreasing C) increasing
; decreasing D) increasing
; decreasing Question
Find the intervals where the function is increasing and decreasing. Use this information to determine all local extrema. 
A) decreasing:
increasing: 
local maximum 
B) decreasing:
increasing: 
local minimum 
C) decreasing:
no extrema
D) increasing:
no extrema
A) decreasing:
increasing: local maximum B) decreasing:
increasing: local minimum C) decreasing:
no extremaD) increasing:
no extrema Question
Find the x-coordinates of all extrema and sketch the graph of 
showing global and local behavior. Round answer to nearest thousandth. 
showing global and local behavior. Round answer to nearest thousandth. Question
Find the x-coordinates of all extrema and sketch the graph of 
showing global and local behavior. 
showing global and local behavior. Question
Question
Using a calculator or computer, estimate the absolute extrema of 
, on the interval 
.
A) absolute max:
; absolute min: 
B) absolute max:
; absolute min: 
C) absolute max:
; absolute min: 
D) absolute max:
; absolute min: 
, on the interval .A) absolute max:
; absolute min: B) absolute max:
; absolute min: C) absolute max:
; absolute min: D) absolute max:
; absolute min: Question
Sketch a graph of a function with the following properties. 
if 
if 
if if Question
Estimate critical numbers and sketch graphs showing both global and local behavior. 
Question
Determine, by hand, all critical numbers of 
and use the First Derivative Test to classify each as a local minimum, local maximum or neither.
A) local maximum at
local minimum at 
Neither at
B) local maximum at
local minimum at 
Neither at
C) local maximum:
local minimum: 
Neither at
D) local maximum:
local minimum: 
Neither at
and use the First Derivative Test to classify each as a local minimum, local maximum or neither.A) local maximum at
local minimum at Neither at
B) local maximum at
local minimum at Neither at
C) local maximum:
local minimum: Neither at
D) local maximum:
local minimum: Neither at
Question
Find all critical numbers of 
and use the First Derivative Test to classify each as a local minimum, local maximum or neither.
A) local maximum: none local minimum: none
Neither at
B) local maximum at
local minimum at 
Neither at
C) local maximum at
local minimum at 
Neither at
D) local maximum: none local minimum at
Neither at
and 
and use the First Derivative Test to classify each as a local minimum, local maximum or neither.A) local maximum: none local minimum: none
Neither at
B) local maximum at
local minimum at Neither at
C) local maximum at
local minimum at Neither at
D) local maximum: none local minimum at
Neither at
and Question
Determine, by hand, the interval(s) where 
is increasing and/or decreasing.
A) increasing
and 
; decreasing 
B) increasing
; decreasing 
C) increasing
and 
; decreasing 
and 
D) increasing
; decreasing 
and 
is increasing and/or decreasing.A) increasing
and ; decreasing B) increasing
; decreasing C) increasing
and ; decreasing and D) increasing
; decreasing and Question
Determine, by hand, the interval(s) where 
is increasing and/or decreasing.
A) increasing
; decreasing 
B) increasing
and 
; decreasing 
and 
C) increasing
and 
; decreasing 
and 
D) increasing
and 
; decreasing 
is increasing and/or decreasing.A) increasing
; decreasing B) increasing
and ; decreasing and C) increasing
and ; decreasing and D) increasing
and ; decreasing Question
Using the critical numbers of 
, use the Second Derivative Test to determine all local extrema.
, use the Second Derivative Test to determine all local extrema. Question
Graph the function and completely discuss the graph. 
A) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: 
; concave down: 
; x-intercept: none 
B) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: 
; concave down: 
x-intercept: none 
C) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: 
; concave up: 
x-intercept: none 
D) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: 
; concave up: 
; x-intercept: none 
A) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: ; concave down: ; x-intercept: none B) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: ; concave down: x-intercept: none C) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: ; concave up: x-intercept: none D) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: ; concave up: ; x-intercept: none Question
Sketch the graph of 
while answering the following questions.
a. What is the domain and range of
?
b. What are the intercepts of
?
c. What, if any, are the equation(s) of vertical asymptotes of
?
d. What, if any, are the local min(s) and local max(s) of
?
e. What, if any, are the inflection point(s) of
?
f. What, if it exists, is the equation of the horizontal asymptote of
? 
while answering the following questions.a. What is the domain and range of
?b. What are the intercepts of
?c. What, if any, are the equation(s) of vertical asymptotes of
?d. What, if any, are the local min(s) and local max(s) of
?e. What, if any, are the inflection point(s) of
?f. What, if it exists, is the equation of the horizontal asymptote of
? Question
Graph the function and completely discuss the graph. 
Question
Estimate the intervals where the function shown below is concave up and/or concave down. 
A) concave up for
concave down for 
B) concave up for
concave down for 
C) concave up for
concave down for 
D) concave up for
concave down for 
A) concave up for
concave down for B) concave up for
concave down for C) concave up for
concave down for D) concave up for
concave down for Question
Estimate the intervals where the function shown below is concave up and/or concave down. 
A) concave up for
concave down for 
B) concave up for
concave down for 
C) concave up for
concave down for 
D) concave up for
concave down for 
A) concave up for
concave down for B) concave up for
concave down for C) concave up for
concave down for D) concave up for
concave down for Question
The unit price of x units of a certain product is given by 
. What is the maximum possible revenue when selling x units? Round answer to nearest dollar.
A)
B)
C)
D)
. What is the maximum possible revenue when selling x units? Round answer to nearest dollar.A)
B)
C)
D)
Question
Sketch the graph with the given properties. 
for all x, 
for 
for 
A)
B)
C)
D)
for all x, for for A)
B)
C)
D)
Question
Graph the function and completely discuss the graph. 
Question
Determine the following significant features by hand and sketch the graph of 
.
a). intercepts
b). asymptotes
c). extrema
d). inflection points
.a). intercepts
b). asymptotes
c). extrema
d). inflection points
Question
Graph the function and completely discuss the graph. Round answers to three decimals places, if necessary. 
A) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: (0, 0), (14, -121.985); concave down: 
;
Concave up:
; x-intercepts: (0, 0) and (35, 0) 
B) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: (0, 0), (14, -121.985); concave up: 
X-intercepts: (0, 0) and (35, 0)
C) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: x = 0; local extrema: (0, 0), (14, -121.985); concave up: 
X-intercepts: (0, 0) and (35, 0)
D) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: x = 0; local extrema: (0, 0), (14, -121.985); concave down: 
;
Concave up:
; x-intercepts: (0, 0) and (35, 0) 
A) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: (0, 0), (14, -121.985); concave down: ;Concave up:
; x-intercepts: (0, 0) and (35, 0) B) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: (0, 0), (14, -121.985); concave up: X-intercepts: (0, 0) and (35, 0)
C) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: x = 0; local extrema: (0, 0), (14, -121.985); concave up: X-intercepts: (0, 0) and (35, 0)
D) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: x = 0; local extrema: (0, 0), (14, -121.985); concave down: ;Concave up:
; x-intercepts: (0, 0) and (35, 0) Question
Determine the intervals where 
is concave up and concave down. Round answers to nearest hundredth.
A) concave up for
concave down for 
B) concave down for
concave up for 
C) concave up for
D) concave down for
concave up for 
is concave up and concave down. Round answers to nearest hundredth.A) concave up for
concave down for B) concave down for
concave up for C) concave up for
D) concave down for
concave up for Question
Determine all significant features and sketch a graph. 
Question
The total cost of producing and marketing x number of units of a certain product is given by 
. For what number x is the total cost a minimum? Round answer to nearest unit.
A)
B)
C)
D)
. For what number x is the total cost a minimum? Round answer to nearest unit.A)
B)
C)
D)
Question
Determine all significant features and sketch a graph. 
Question
Estimate the intervals where the function shown below is concave up and/or concave down. 
A) concave up for
concave down for 
B) concave up for
concave down for 
C) concave up for
concave down for 
D) concave up for
concave down for 
A) concave up for
concave down for B) concave up for
concave down for C) concave up for
concave down for D) concave up for
concave down for Question
Determine all significant features and sketch a graph. 
Question
Sketch the graph of 
while answering the following questions.
a. What is the domain and range of
?
b. What are the intercepts of
?
c. What, if any, are the equation(s) of vertical asymototes of
?
d. What, if any, are the local min(s) and local max(s) of
?
e. What, if any, are the inflection point(s) of
?
f. What, if it exists, is the equation of the horizontal asymotote of
? 
while answering the following questions.a. What is the domain and range of
?b. What are the intercepts of
?c. What, if any, are the equation(s) of vertical asymototes of
?d. What, if any, are the local min(s) and local max(s) of
?e. What, if any, are the inflection point(s) of
?f. What, if it exists, is the equation of the horizontal asymotote of
? Question
Using the critical numbers of 
, use the Second Derivative Test to determine all local extrema.
A) critical numbers:
; local max 
; local min 
B) critical numbers:
; local max 
; local min 
C) critical numbers:
; local max 
; local min 
D) critical numbers:
; local max 
; local min 
, use the Second Derivative Test to determine all local extrema.A) critical numbers:
; local max ; local min B) critical numbers:
; local max ; local min C) critical numbers:
; local max ; local min D) critical numbers:
; local max ; local min Question
Determine all significant features by hand and sketch the graph of 
.
a). intercepts
b). asymptotes
c). extrema
d). inflection points
.a). intercepts
b). asymptotes
c). extrema
d). inflection points
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Deck 4: Applications of the Derivative
1
Given the graph of , locate the absolute extrema (if they exist) on the interval .
A) absolute max:
B) absolute min:
C) absolute min:
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max:
B) absolute min:
C) absolute min:
D) no absolute extrema
absolute max:
2
Using Newton's method with , determine the third iteration when approximating the root to at least six-digit accuracy of the following equation. x3 + x2 - 5x + 4 = 0
A) -3.062500
B) -3.060647
C) -3.060691
D) -3.060992
, determine the third iteration when approximating the root to at least six-digit accuracy of the following equation. x3 + x2 - 5x + 4 = 0A) -3.062500
B) -3.060647
C) -3.060691
D) -3.060992
-3.060647
3
Find the linear approximation, L(x), to f(x) at x = x0.
A)
B)
C)
D)
A)
B)
C)
D)
4
Given the graph of , locate the absolute extrema (if they exist) on the interval .
A) absolute max:
B) absolute min: and
C) absolute min:
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max:
B) absolute min:
and C) absolute min:
D) no absolute extrema
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5
Given the graph of , locate the absolute extrema (if they exist) on the interval .
A) absolute max:
B) absolute min: and
C) absolute min:
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max:
B) absolute min:
and C) absolute min:
D) no absolute extrema
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6
Find the linear approximation at x = 0 to show that the following commonly used approximation is valid for "small" x.
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7
Use linear approximation of at to estimate the quantity of to the nearest ten thousandth.
A)
B)
C)
D)
at to estimate the quantity of to the nearest ten thousandth.A)
B)
C)
D)
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8
Use a linear approximation to estimate
A) 0
B) 0.18
C) 0.1
D) 0.02
A) 0
B) 0.18
C) 0.1
D) 0.02
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9
Use a linear approximation to estimate Note that 17.2 is near 16 which is
A) 3.23649
B) 2.03649
C) 2.0375
D) 3.08312
Note that 17.2 is near 16 which is A) 3.23649
B) 2.03649
C) 2.0375
D) 3.08312
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10
Use Newton's method with x0 = 2.6 to compute x1 and x2 without the use of a calculator.
f(x) = x3 - 3x - 5
f(x) = x3 - 3x - 5
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11
A certain company estimates that it can sell f(x)-thousand video game consoles at the price of $x as given in the table. Use a linear approximation to estimate the number of consoles that can be sold at $62.
A) approximately 105 thousand consoles
B) approximately 108 thousand consoles
C) approximately 130 thousand consoles
D) approximately 138 thousand consoles
Use a linear approximation to estimate the number of consoles that can be sold at $62.A) approximately 105 thousand consoles
B) approximately 108 thousand consoles
C) approximately 130 thousand consoles
D) approximately 138 thousand consoles
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12
Find the linear approximation at x = 0 for each of f (x) = (x + 1)2 + 5, g(x) = 6 + sin(2x) and . Graph each function together with its linear approximation.
. Graph each function together with its linear approximation. Unlock Deck
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13
Use Newton's method to find an approximate root of the equation (accurate to six decimal places).
A) 0.306232
B) 0.216232
C) 0.136232
D) 0.219565
(accurate to six decimal places).A) 0.306232
B) 0.216232
C) 0.136232
D) 0.219565
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14
-The impedance Z of a simple RL (resistive inductive) circuit is given by
, where R is the resistance of the resistor, L is the inductance of the inductor, and is the angular frequency of the applied voltage. Find a linear approximation of Z(L) for small values of L assuming all other quantities are constant. Show all of your work. Unlock Deck
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15
Find the linear approximation, L(x), to f(x) at x = x0.
A)
B)
C)
D)
A)
B)
C)
D)
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16
Approximate accurate to 3 decimal places using Newton's method. State the function used.
A) 2.289 using
B) 2.359 using
C) 2.219 using
D) 2.289 using
accurate to 3 decimal places using Newton's method. State the function used.A) 2.289 using
B) 2.359 using
C) 2.219 using
D) 2.289 using
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17
Explain why Newton's method fails for the following equation with the specified initial guess.
A) Using we see that f is not differentiable at
B) Using we obtain .
C) Using we obtain which will give
D) Using we see that f does not have any real roots.
A) Using
we see that f is not differentiable at B) Using
we obtain .C) Using
we obtain which will give D) Using
we see that f does not have any real roots. Unlock Deck
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18
Newton's method fails for the given initial guess. Explain why the method fails and, if possible, find a root by correcting the problem. Round to four decimal places, if necessary. , x0 = -1
A) f '(-1) = 0; -1.905, 0.105
B) f '(-1) does not exist; -1.905, 0.105
C) f (-1) = 0; 1.905, -0.105
D) f (-1) does not exist; 1.905, -0.105
, x0 = -1A) f '(-1) = 0; -1.905, 0.105
B) f '(-1) does not exist; -1.905, 0.105
C) f (-1) = 0; 1.905, -0.105
D) f (-1) does not exist; 1.905, -0.105
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19
Given the graph of f(x), draw in the tangent lines used in Newton's method to determine x1 and x2 after starting at x0 = 1.
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20
Using Newton's method, approximate the root of the following equation to at least six-digit accuracy. x3 + x2 - 3x + 5 = 0
A) -2.777778
B) -2.774551
C) -2.751101
D) -2.757031
A) -2.777778
B) -2.774551
C) -2.751101
D) -2.757031
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21
Given the graph of , locate the absolute extrema (if they exist) on the interval .
A) absolute max: absolute min:
B) absolute max: absolute min:
C) absolute max: absolute min:
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max:
absolute min: B) absolute max:
absolute min: C) absolute max:
absolute min: D) no absolute extrema
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22
Given determine if the critical number represents a local maximum, local minimum or neither.
A) local maximum
B) local minimum
C) neither
determine if the critical number represents a local maximum, local minimum or neither.A) local maximum
B) local minimum
C) neither
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23
Given determine if the critical number represents a local maximum, local minimum or neither.
A) local maximum
B) local minimum
C) neither
determine if the critical number represents a local maximum, local minimum or neither.A) local maximum
B) local minimum
C) neither
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24
Find the absolute extrema of the given function on the indicated interval. on
A) absolute maxima: , absolute minimum:
B) absolute maximum: , absolute minimum:
C) absolute maximum: , absolute minimum:
D) absolute maximum: , absolute minimum:
on A) absolute maxima:
, absolute minimum: B) absolute maximum:
, absolute minimum: C) absolute maximum:
, absolute minimum: D) absolute maximum:
, absolute minimum: Unlock Deck
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25
Given the graph of , locate the absolute extrema (if they exist) on the interval .
A) absolute max: absolute min:
B) absolute min:
C) absolute max: absolute min:
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max:
absolute min: B) absolute min:
C) absolute max:
absolute min: D) no absolute extrema
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26
Given , determine the critical number(s).
A)
B)
C)
D)
, determine the critical number(s).A)
B)
C)
D)
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27
Given , determine the absolute extrema on the interval .
A) absolute max: ; absolute min:
B) absolute max: and ; absolute min: and
C) absolute max: ; absolute min:
D) absolute max: ; absolute min:
, determine the absolute extrema on the interval .A) absolute max:
; absolute min: B) absolute max:
and ; absolute min: and C) absolute max:
; absolute min: D) absolute max:
; absolute min: Unlock Deck
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28
Given , on the interval , determine if the critical number represents a local maximum, local minimum or neither.
A) local maximum
B) local minimum
C) neither
, on the interval , determine if the critical number represents a local maximum, local minimum or neither.A) local maximum
B) local minimum
C) neither
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29
Given determine the critical number(s).
A)
B)
C)
D)
determine the critical number(s).A)
B)
C)
D)
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30
Given the graph of , locate the absolute extrema (if they exist) on the interval .
A) absolute max: approximately absolute min:
B) absolute max: absolute min:
C) absolute max: absolute min:
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max: approximately
absolute min: B) absolute max:
absolute min: C) absolute max:
absolute min: D) no absolute extrema
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31
Find all critical numbers.
A)
B) ,
C)
D)
A)
B)
, C)
D)
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32
Given the graph of , locate the absolute extrema (if they exist) on the interval .
A) absolute max: approximately
B) absolute max: approximately absolute min:
C) absolute max: approximately absolute min:
Absolute min:
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max: approximately
B) absolute max: approximately
absolute min: C) absolute max: approximately
absolute min: Absolute min:
D) no absolute extrema
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33
Determine all critical numbers of .
A)
B)
C)
D)
.A)
B)
C)
D)
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34
Find all critical numbers. Then use a graph to determine whether the critical numbers represent a local maximum, local minimum, or neither.
A) (local maximum), (neither), (local minimum)
B) (local maximum), (local maximum), (local minimum)
C) (local maximum), (local minimum)
D) (local minimum), (local maximum)
A)
(local maximum), (neither), (local minimum)B)
(local maximum), (local maximum), (local minimum)C)
(local maximum), (local minimum)D)
(local minimum), (local maximum) Unlock Deck
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35
Given the graph of , locate the absolute extrema (if they exist) on the interval .
A) absolute max: absolute min:
B) absolute min:
C) absolute max: absolute min:
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max:
absolute min: B) absolute min:
C) absolute max:
absolute min: D) no absolute extrema
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36
Find the absolute extrema of the given function on the indicated interval. on
A) absolute maximum: , absolute minimum:
B) absolute maximum: , absolute minimum:
C) absolute maximum: , absolute minimum:
D) absolute maximum: , absolute minimum:
on A) absolute maximum:
, absolute minimum: B) absolute maximum:
, absolute minimum: C) absolute maximum:
, absolute minimum: D) absolute maximum:
, absolute minimum: Unlock Deck
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37
Given the graph of , locate the absolute extrema (if they exist) on the interval .
A) absolute max: approximately
B) absolute max: absolute min:
C) absolute max: absolute min:
D) no absolute extrema
, locate the absolute extrema (if they exist) on the interval . A) absolute max: approximately
B) absolute max:
absolute min: C) absolute max:
absolute min: D) no absolute extrema
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38
Determine all critical numbers of .
A)
B)
C)
D)
.A)
B)
C)
D)
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39
Given , on the interval , determine the critical number(s).
A)
B)
C)
D)
, on the interval , determine the critical number(s).A)
B)
C)
D)
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40
Find all critical numbers by hand. f (x) = x4/3 + 4x1/3 + 24x-2/3
A) -4, 0, 3
B) -4, 3
C) 0
D) -3, 0, 4
A) -4, 0, 3
B) -4, 3
C) 0
D) -3, 0, 4
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41
Find the intervals where the function is increasing and decreasing on the specified interval. Use this information to determine all local extrema. on
on Unlock Deck
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42
Determine the intervals where is concave up and concave down.
A) concave down for concave up for
B) concave down for concave up for
C) concave down for cancave up for
D) concave down for and concave up for
is concave up and concave down.A) concave down for
concave up for B) concave down for
concave up for C) concave down for
cancave up for D) concave down for
and concave up for Unlock Deck
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43
Using a calculator or computer, estimate the absolute extrema of on the interval . Round answer to the nearest hundredth.
A) absolute max: ; absolute min:
B) absolute max: ; absolute min:
C) absolute max: ; absolute min:
D) absolute max: ; absolute min:
on the interval . Round answer to the nearest hundredth.A) absolute max:
; absolute min: B) absolute max:
; absolute min: C) absolute max:
; absolute min: D) absolute max:
; absolute min: Unlock Deck
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44
Find all asymptotes and extrema and sketch a graph.
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45
Determine, by hand, all critical numbers of and use the First Derivative Test to classify each as a local minimum, local maximum or neither.
A) local maximum at local minimum at
Neither:
B) local maximum at local minimum at
Neither:
C) local maximum at local minimum at
Neither:
D) local maximum at local minimum at
Neither:
and use the First Derivative Test to classify each as a local minimum, local maximum or neither.A) local maximum at
local minimum at Neither:
B) local maximum at
local minimum at Neither:
C) local maximum at
local minimum at Neither:
D) local maximum at
local minimum at Neither:
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46
Find all asymptotes and extrema and sketch a graph.
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47
A herd of ninety-nine antelope is released onto a small game reserve so that their reproductive habits can be studied. In the beginning the population of the herd increases rapidly in size but eventually slows due to a dwindling food supply. Suppose the population of antelope after t years is given by the function where . Determine when the population begins to decline.
A) 15 years
B) 17 years
C) 18 years
D) 19 years
where . Determine when the population begins to decline.A) 15 years
B) 17 years
C) 18 years
D) 19 years
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48
Find the x-coordinates of all extrema and sketch the graph showing global and local behavior of the function. Round answers to nearest thousandth. y = x5 - 150x3 + 460x + 9
A) local max: x = -1.017, x = 9.432 local min: x = -9.432, x = 1.017
B) local max: x = -9.432, x = 1.017 local min: x = -1.017, x = 9.432
C) local max: x = -1.0343 local min: x = 1.0343
D) local max: x = 1.0343 local min: x = -1.0343
A) local max: x = -1.017, x = 9.432 local min: x = -9.432, x = 1.017
B) local max: x = -9.432, x = 1.017 local min: x = -1.017, x = 9.432
C) local max: x = -1.0343 local min: x = 1.0343
D) local max: x = 1.0343 local min: x = -1.0343
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49
Determine, by hand, the interval(s) where is increasing and/or decreasing.
A)
B) increasing ; decreasing
C) increasing ; decreasing
D) increasing ; decreasing
is increasing and/or decreasing.A)
B) increasing
; decreasing C) increasing
; decreasing D) increasing
; decreasing Unlock Deck
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50
Find the intervals where the function is increasing and decreasing. Use this information to determine all local extrema.
A) decreasing: increasing: local maximum
B) decreasing: increasing: local minimum
C) decreasing: no extrema
D) increasing: no extrema
A) decreasing:
increasing: local maximum B) decreasing:
increasing: local minimum C) decreasing:
no extremaD) increasing:
no extrema Unlock Deck
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51
Find the x-coordinates of all extrema and sketch the graph of showing global and local behavior. Round answer to nearest thousandth.
showing global and local behavior. Round answer to nearest thousandth. Unlock Deck
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52
Find the x-coordinates of all extrema and sketch the graph of showing global and local behavior.
showing global and local behavior. Unlock Deck
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53
Find (by hand) all critical numbers and use the First Derivative Test to classify each as the location of a local maximum, local minimum or neither. y = x4/3 - 8x1/3 - 6
A) x = 0 (neither)
B) x = -2 (local maxima)
C) x = -2 (local minima)
D) x = 2 (local minima), x = 0 (neither)
A) x = 0 (neither)
B) x = -2 (local maxima)
C) x = -2 (local minima)
D) x = 2 (local minima), x = 0 (neither)
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54
Using a calculator or computer, estimate the absolute extrema of , on the interval .
A) absolute max: ; absolute min:
B) absolute max: ; absolute min:
C) absolute max: ; absolute min:
D) absolute max: ; absolute min:
, on the interval .A) absolute max:
; absolute min: B) absolute max:
; absolute min: C) absolute max:
; absolute min: D) absolute max:
; absolute min: Unlock Deck
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55
Sketch a graph of a function with the following properties. if if
if if Unlock Deck
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56
Estimate critical numbers and sketch graphs showing both global and local behavior.
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57
Determine, by hand, all critical numbers of and use the First Derivative Test to classify each as a local minimum, local maximum or neither.
A) local maximum at local minimum at
Neither at
B) local maximum at local minimum at
Neither at
C) local maximum: local minimum:
Neither at
D) local maximum: local minimum:
Neither at
and use the First Derivative Test to classify each as a local minimum, local maximum or neither.A) local maximum at
local minimum at Neither at
B) local maximum at
local minimum at Neither at
C) local maximum:
local minimum: Neither at
D) local maximum:
local minimum: Neither at
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58
Find all critical numbers of and use the First Derivative Test to classify each as a local minimum, local maximum or neither.
A) local maximum: none local minimum: none
Neither at
B) local maximum at local minimum at
Neither at
C) local maximum at local minimum at
Neither at
D) local maximum: none local minimum at
Neither at and
and use the First Derivative Test to classify each as a local minimum, local maximum or neither.A) local maximum: none local minimum: none
Neither at
B) local maximum at
local minimum at Neither at
C) local maximum at
local minimum at Neither at
D) local maximum: none local minimum at
Neither at
and Unlock Deck
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59
Determine, by hand, the interval(s) where is increasing and/or decreasing.
A) increasing and ; decreasing
B) increasing ; decreasing
C) increasing and ; decreasing and
D) increasing ; decreasing and
is increasing and/or decreasing.A) increasing
and ; decreasing B) increasing
; decreasing C) increasing
and ; decreasing and D) increasing
; decreasing and Unlock Deck
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60
Determine, by hand, the interval(s) where is increasing and/or decreasing.
A) increasing ; decreasing
B) increasing and ; decreasing and
C) increasing and ; decreasing and
D) increasing and ; decreasing
is increasing and/or decreasing.A) increasing
; decreasing B) increasing
and ; decreasing and C) increasing
and ; decreasing and D) increasing
and ; decreasing Unlock Deck
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61
Using the critical numbers of , use the Second Derivative Test to determine all local extrema.
, use the Second Derivative Test to determine all local extrema. Unlock Deck
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62
Graph the function and completely discuss the graph.
A) domain: vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: ; concave down: ; x-intercept: none
B) domain: vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: ; concave down: x-intercept: none
C) domain: vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: ; concave up: x-intercept: none
D) domain: vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: ; concave up: ; x-intercept: none
A) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: ; concave down: ; x-intercept: none B) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: ; concave down: x-intercept: none C) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: ; concave up: x-intercept: none D) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: ; concave up: ; x-intercept: none Unlock Deck
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63
Sketch the graph of while answering the following questions.
a. What is the domain and range of ?
b. What are the intercepts of ?
c. What, if any, are the equation(s) of vertical asymptotes of ?
d. What, if any, are the local min(s) and local max(s) of ?
e. What, if any, are the inflection point(s) of ?
f. What, if it exists, is the equation of the horizontal asymptote of ?
while answering the following questions.a. What is the domain and range of
?b. What are the intercepts of
?c. What, if any, are the equation(s) of vertical asymptotes of
?d. What, if any, are the local min(s) and local max(s) of
?e. What, if any, are the inflection point(s) of
?f. What, if it exists, is the equation of the horizontal asymptote of
? Unlock Deck
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64
Graph the function and completely discuss the graph.
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65
Estimate the intervals where the function shown below is concave up and/or concave down.
A) concave up for concave down for
B) concave up for concave down for
C) concave up for concave down for
D) concave up for concave down for
A) concave up for
concave down for B) concave up for
concave down for C) concave up for
concave down for D) concave up for
concave down for Unlock Deck
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66
Estimate the intervals where the function shown below is concave up and/or concave down.
A) concave up for concave down for
B) concave up for concave down for
C) concave up for concave down for
D) concave up for concave down for
A) concave up for
concave down for B) concave up for
concave down for C) concave up for
concave down for D) concave up for
concave down for Unlock Deck
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67
The unit price of x units of a certain product is given by . What is the maximum possible revenue when selling x units? Round answer to nearest dollar.
A)
B)
C)
D)
. What is the maximum possible revenue when selling x units? Round answer to nearest dollar.A)
B)
C)
D)
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68
Sketch the graph with the given properties. for all x, for for
A)
B)
C)
D)
for all x, for for A)
B)
C)
D)
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69
Graph the function and completely discuss the graph.
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70
Determine the following significant features by hand and sketch the graph of .
a). intercepts
b). asymptotes
c). extrema
d). inflection points
.a). intercepts
b). asymptotes
c). extrema
d). inflection points
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71
Graph the function and completely discuss the graph. Round answers to three decimals places, if necessary.
A) domain: vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: (0, 0), (14, -121.985); concave down: ;
Concave up: ; x-intercepts: (0, 0) and (35, 0)
B) domain: vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: (0, 0), (14, -121.985); concave up:
X-intercepts: (0, 0) and (35, 0)
C) domain: vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: x = 0; local extrema: (0, 0), (14, -121.985); concave up:
X-intercepts: (0, 0) and (35, 0)
D) domain: vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: x = 0; local extrema: (0, 0), (14, -121.985); concave down: ;
Concave up: ; x-intercepts: (0, 0) and (35, 0)
A) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: (0, 0), (14, -121.985); concave down: ;Concave up:
; x-intercepts: (0, 0) and (35, 0) B) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: none; local extrema: (0, 0), (14, -121.985); concave up: X-intercepts: (0, 0) and (35, 0)
C) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: x = 0; local extrema: (0, 0), (14, -121.985); concave up: X-intercepts: (0, 0) and (35, 0)
D) domain:
vertical asymptotes: none; horizontal asymptotes: none; vertical tangents: x = 0; local extrema: (0, 0), (14, -121.985); concave down: ;Concave up:
; x-intercepts: (0, 0) and (35, 0) Unlock Deck
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72
Determine the intervals where is concave up and concave down. Round answers to nearest hundredth.
A) concave up for concave down for
B) concave down for concave up for
C) concave up for
D) concave down for concave up for
is concave up and concave down. Round answers to nearest hundredth.A) concave up for
concave down for B) concave down for
concave up for C) concave up for
D) concave down for
concave up for Unlock Deck
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73
Determine all significant features and sketch a graph.
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74
The total cost of producing and marketing x number of units of a certain product is given by . For what number x is the total cost a minimum? Round answer to nearest unit.
A)
B)
C)
D)
. For what number x is the total cost a minimum? Round answer to nearest unit.A)
B)
C)
D)
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75
Determine all significant features and sketch a graph.
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76
Estimate the intervals where the function shown below is concave up and/or concave down.
A) concave up for concave down for
B) concave up for concave down for
C) concave up for concave down for
D) concave up for concave down for
A) concave up for
concave down for B) concave up for
concave down for C) concave up for
concave down for D) concave up for
concave down for Unlock Deck
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77
Determine all significant features and sketch a graph.
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78
Sketch the graph of while answering the following questions.
a. What is the domain and range of ?
b. What are the intercepts of ?
c. What, if any, are the equation(s) of vertical asymototes of ?
d. What, if any, are the local min(s) and local max(s) of ?
e. What, if any, are the inflection point(s) of ?
f. What, if it exists, is the equation of the horizontal asymotote of ?
while answering the following questions.a. What is the domain and range of
?b. What are the intercepts of
?c. What, if any, are the equation(s) of vertical asymototes of
?d. What, if any, are the local min(s) and local max(s) of
?e. What, if any, are the inflection point(s) of
?f. What, if it exists, is the equation of the horizontal asymotote of
? Unlock Deck
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79
Using the critical numbers of , use the Second Derivative Test to determine all local extrema.
A) critical numbers: ; local max ; local min
B) critical numbers: ; local max ; local min
C) critical numbers: ; local max ; local min
D) critical numbers: ; local max ; local min
, use the Second Derivative Test to determine all local extrema.A) critical numbers:
; local max ; local min B) critical numbers:
; local max ; local min C) critical numbers:
; local max ; local min D) critical numbers:
; local max ; local min Unlock Deck
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80
Determine all significant features by hand and sketch the graph of .
a). intercepts
b). asymptotes
c). extrema
d). inflection points
.a). intercepts
b). asymptotes
c). extrema
d). inflection points
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