# Quiz 4: Applications of Differentiation

Mathematics

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Multiple Choice

C

Q 2Q 2

Given that the graph of f passes through the point (4, 69) and that the slope of its tangent line at is , find f (1) .
A)11
B)0
C)6
D)12
E)1

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C

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B

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Q 7Q 7

What constant acceleration is required to increase the speed of a car from 20 ft/s to 45 ft/s in s?

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Q 8Q 8

A car braked with a constant deceleration of 40 , producing skid marks measuring 60 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?

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Q 9Q 9

Find the position function of a particle moving along a coordinate line that satisfies the given conditions. , s (0) = 5, v (0) = 0

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Q 10Q 10

Find the position function of a particle moving along a coordinate line that satisfies the given condition. , s(1) = -1

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Q 11Q 11

Use Newton's method with the specified initial approximation to find , the third approximation to the root of the given equation. (Round your answer to four decimal places.)
A)
B)
C)
D)
E)

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Q 12Q 12

Use Newton's method with the specified initial approximation to find , the third approximation to the root of the given equation. (Round your answer to four decimal places.)
A)
B)
C)
D)
E)

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Q 13Q 13

Use Newton's method to approximate the given number correct to eight decimal places.
A)
B)
C)
D)
E)

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Q 14Q 14

Use Newton's method with the specified initial approximation to find , the third approximation to the root of the given equation. (Give your answer to four decimal places.)

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Q 15Q 15

Use Newton's method to approximate the indicated root of in the interval , correct to six decimal places.Use as the initial approximation.

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Q 16Q 16

Find two positive numbers whose product is and whose sum is a minimum.
A)
B)3, 48
C)
D)6, 24
E)2, 72

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Q 18Q 18

A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.
A)4.35 m
B)3.25 m
C)0 m
D)5.35 m
E)4.4 m

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Multiple Choice

Q 19Q 19

A woman at a point A on the shore of a circular lake with radius wants to arrive at the point C diametrically opposite on the other side of the lake in the shortest possible time. She can walk at the rate of and row a boat at . How should she proceed? (Find ). Round the result, if necessary, to the nearest hundredth.
A) radians
B)She should row from point A to point C radians
C) radians
D) radians
E)She should walk around the lake from point A to point C.

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Q 20Q 20

The sum of two positive numbers is . What is the smallest possible value of the sum of their squares?

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Q 22Q 22

A farmer with 710 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?

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Q 23Q 23

Find an equation of the line through the point that cuts off the least area from the first quadrant.

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Q 24Q 24

A steel pipe is being carried down a hallway 14 ft wide. At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide. What is the length of the longest pipe that can be carried horizontally around the corner?

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Q 25Q 25

Find the maximum area of a rectangle that can be circumscribed about a given rectangle with length L = 8 and width W = 3.

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Q 26Q 26

Use the guidelines of this section to sketch the curve. Select the graph of the curve.
A)
D)
B)
E)
C)

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Q 27Q 27

Use the guidelines of this section to sketch the curve. Select the graph of the curve.
A)
D)
B)
E)
C)

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Q 28Q 28

Use the guidelines of this section to sketch the curve. Select the graph of the curve.
A)
D)
B)
E)
C)

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Q 29Q 29Use the guidelines of this section to sketch the curve. Select the graph of the curve.
A)
D)
B)
E)
C)

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Q 30Q 30Use the guidelines of this section to sketch the curve. Select the graph of the curve.
A)
D)
B)
E)
C)

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Q 31Q 31

Given .(a) Find the intervals on which f is increasing or decreasing.(b) Find the relative maxima and relative minima of
F)
A)(a) Increasing on ,
Decreasing on
(b) Rel. max.
B)(a) Increasing on ,
Decreasing on
(b) Rel. min.
C)(a) Increasing on ,
Decreasing on
(b) Rel. max.
D)(a) Increasing on ,
Decreasing on
(b) Rel. min.

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Q 32Q 32

Given .(a) Find the intervals on which f is increasing or decreasing.(b) Find the relative maxima and relative minima of
F)
A)(a) Increasing on and
decreasing on
(b) Rel. max. ,
Rel) min.
B)(a) Increasing on , decreasing on
and
(b) Rel. max. ,
Rel) min.
C)(a) Increasing on and
decreasing on
(b) Rel. max. ,
Rel) min.
D)(a) Increasing on , decreasing on
and
(b) Rel. max. ,
Rel) min.

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Multiple Choice

Q 33Q 33

Determine where the graph of the function is concave upward and where it is concave downward. Also, find all inflection points of the function.
A)CU on , CD on
,
IP
B)CU on , CD on
and
IP
and
C)CU on , CD on
,
IP
D)CU on , CD on
,
IP

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Multiple Choice

Q 34Q 34

Given .(a) Find the intervals on which f is increasing or decreasing.(b) Find the relative maxima and relative minima of
F)
A)(a) Increasing on and
, decreasing on
(b) Rel. max. ,
Rel) min.
B)(a) Increasing on and
, decreasing on
and
(b) Rel. max. ,
Rel) min.
C)(a) Increasing on , decreasing on
and
(b) Rel. max. ,
Rel) min.
D)(a) Increasing on and
decreasing on
and
(b) Rel. max. ,
Rel) min.

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Q 35Q 35

Use the Second Derivative Test to find the relative extrema, if any, of the function .
A)Rel. max. , rel. min.
B)Rel. max. , rel. min.
C)Rel. max. , rel. min.
D)Rel. max. , rel. min.

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Q 36Q 36

The graph of the derivative of a continuous function f is shown. On what intervals is f decreasing? .
A)
B)
C)
D)
E)None of these

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Q 38Q 38

Given .(a) Find the intervals on which f is increasing or decreasing.(b) Find the relative maxima and relative minima of
F)
A)(a) Increasing on ,
Decreasing on
(b) Rel. max.
B)(a) Increasing on
(b) None
C)(a) Decreasing on
(b) None
D)(a) Increasing on ,
Decreasing on
(b) Rel. min.

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Multiple Choice

Q 39Q 39

Determine where the graph of the function is concave upward and where it is concave downward. Also, find all inflection points of the function.
A)CU on , CD on
,
IP
B)CU on , CD on
,
IP
C)CU on , CD on
,
IP
D)CU on , CD on
,
IP

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Multiple Choice

Q 40Q 40

Determine where the graph of is concave upward and where it is concave downward. Also, find all inflection points of the function.
A)concave downward: and
, concave upward:
and
; inflection points:
and
B)concave downward: and
, concave upward:
and
; inflection points:
and
C)concave downward: nowhere, concave upward: and
; inflection points: none
D)concave downward: and
, concave upward: nowhere; inflection points: none

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Q 41Q 41

The graph of the first derivative of a function f is shown below. At what values of x does f have a local maximum or minimum?

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Q 43Q 43

Find a cubic function that has a local maximum value of at 1 and a local minimum value of -1,184 at 7.

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Q 44Q 44

Determine where the graph of is concave upward and where it is concave downward. Also, find all inflection points of the function.

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Q 45Q 45

Consider the function . (a) Find the intervals on which f is increasing or decreasing. (b) Find the relative maxima and relative minima of F.

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Q 46Q 46

The function satisfies the hypotheses of Rolle's Theorem on the interval . Find all values of c that satisfy the conclusion of the theorem.
A)
B)
C)
D)

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Q 47Q 47

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem.
A)
B)
C)
D)
E)

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Q 48Q 48

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. ,
A)None of these
B) ,
C) ,
D) ,
E) ,

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Multiple Choice

Q 49Q 49

The function satisfies the hypotheses of Rolle's Theorem on the interval . Find all values of c that satisfy the conclusion of the theorem.
A)-6, -4
B)-5, -4
C)-6
D)-5

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Q 50Q 50

The function satisfies the hypotheses of the Mean Value Theorem on the interval . Find all values of c that satisfy the conclusion of the theorem.
A)-7
B)-8, -6
C)-8, -7
D)-6

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Q 51Q 51

Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. ,
A)
B)
C)
D)
E)None of these

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Q 52Q 52

At 4:00 P.M. a car's speedometer reads 25 . At 4:15 it reads 72 . At some time between 4:00 and 4:15 the acceleration is exactly x . Find x.

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Q 59Q 59

Find the absolute maximum and absolute minimum values, if any, of the function on [0, 25]
A)Abs. max. abs. min.
B)Abs. max. abs. min.
C)Abs. max. abs. min.
D)Abs. max. abs. min.

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Q 60Q 60

Find the absolute maximum and absolute minimum values, if any, of the function on .
A)Abs. max. abs. min.
B)Abs. max. abs. min.
C)Abs. max. abs. min.
D)Abs. max. abs. min.

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Q 65Q 65

The graph below is the graph of function f on the interval Find the absolute maximum and absolute minimum values of f (if they exist) and where they are attained.

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