Question 1

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.

Accepted Answer

The second derivative of the function is 22eaa3e5_55d5_8276_9f8f_8a859b3607ec_TB5971_11 which is always positive. Hence, the function is always concave up and any critical point will be a relative minimum. 
Now, to find the relative maximum, we need to look at the behavior of the function around the critical point. The critical point is at x=3. 
Computing the first derivative yields 11eaa3e5_55d5_a27f_9f8f_ed277c5e5db5_TB5971_11 which changes sign from negative to positive as we cross x=3, indicating a local minimum at that point. Therefore, the function has a relative maximum to the left of x=3 and a relative minimum at x=3. 
Using test points to the left and right of x=3 in the first derivative, we can confirm that the relative maximum is at x=1 and has a value of 11eaa3e5_55d4_f74d_9f8f_9be7a9e90cfa_TB5971_11, while the relative minimum at x=3 has a value of 11eaa3e5_55d4_f74e_9f8f_c9175818d242_TB5971_11. Therefore, the answer is B.

Question 2

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

Accepted Answer

The answer of Determine where the graph of the function...

Question 3

You are given the graph of f.  Find the horizontal and vertical asymptotes of the graph of f.

Accepted Answer

The answer of You are given the graph of f....

Question 4

A city's population (in thousands) t years from now is estimated by  What will the population of the city be in the long run? Hint: Find

Accepted Answer

The answer of A city's population (in thousands) t years...

Question 5

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  and  IP  and 
D)CU on  , CD on  , IP

Accepted Answer

The answer of Determine where the graph of the function...

Question 6

Use the graph of f to find the given limits.
(a)  (b)

Accepted Answer

The answer of Use the graph of f to find...

Question 7

Evaluate the limit. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The limit is evaluated by looking at the digits in the exponent. In this case, the digits are "0893", which is the largest value among the answer choices. Therefore, the answer is E.

Question 8

Find the limit.

Accepted Answer

The answer of Find the limit. ...

Question 9

How many points of inflection are on the graph of the function? 
A)3
B)2
C)1
D)5
E)4

Accepted Answer

The answer of How many points of inflection are on...

Question 10

Find the inflection points for the function given.  , 
A)  , 
B)  , 
C)  , 
D)  , 
E)  ,

Accepted Answer

The answer of Find the inflection points for the function...

Question 11

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

Accepted Answer

The answer of Given  . (a) Find the intervals...

Question 12

For the function f whose graph is given, find the limit.

Accepted Answer

The answer of For the function f whose graph is...

Question 13

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.

Accepted Answer

The answer of Given  . (a) Find the intervals...

Question 14

Find the limit.

Accepted Answer

The answer of Find the limit. ...

Question 15

Find the limit.

Accepted Answer

The answer of Find the limit. ...

Question 16

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

Accepted Answer

The answer of The graph of the derivative  of...

Question 17

Find the horizontal and vertical asymptotes of the graph of the function  .

Accepted Answer

The answer of Find the horizontal and vertical asymptotes of...

Question 18

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  and  (b) Rel.max.  ,
Rel)min. 
B)(a) Increasing on  and  decreasing on  (b) Rel.max.  ,
Rel)min. 
C)(a) Increasing on  , decreasing on  and  (b) Rel.max.  ,
Rel)min. 
D)(a) Increasing on  and  decreasing on  (b) Rel.max.  ,
Rel)min.

Accepted Answer

The answer of Given  . (a) Find the intervals...

Question 19

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  and  , IP  and 
B)CU on  and  , CD on  , IP  and 
C)CU on  , IP none
D)CD on  , IP none

Accepted Answer

The answer of Determine where the graph of the function...

Question 20

Let f (x) = 4x³ - 5x² + x - 2 and g (x) = 4x³ a.Plot the graph of f and g using the same viewing window: [-5, 5] ´ [-5, 5]. b.Plot the graph of f and g using the same viewing window: [-50, 50] ´ [-100,000, 100,000] c.Explain why the graphs of f and g that you obtained in part (b) seem coalesce as x increases or decreases without bound.

Accepted Answer

The answer of Let f (x) = 4x³ - 5x²...

Quiz 3: Applications of Differentiation

Use the Second Derivative Test to find the relative extrema, if any, of the function .

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

You are given the graph of f. Find the horizontal and vertical asymptotes of the graph of f.

A city's population (in thousands) t years from now is estimated by What will the population of the city be in the long run? Hint: Find

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

Use the graph of f to find the given limits. (a) (b)

Evaluate the limit.

Find the limit.

How many points of inflection are on the graph of the function?

Find the inflection points for the function given. ,

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

For the function f whose graph is given, find the limit.

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

Find the limit.

Find the limit.

The graph of the derivative of a continuous function f is shown. On what intervals is f decreasing? .

Find the horizontal and vertical asymptotes of the graph of the function .

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

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