Question 1

Find the relative maxima and relative minima, if any, of the function. Otherwise, answer none.
​   ​
Relative minima: __________
​
Relative maxima: __________

Accepted Answer

The answer of Find the relative maxima and relative minima,...

Question 2

The concentration (in milligrams/cubic centimeter) of a certain drug in a patient's body t hr after injection is given by ​     .
​
When is the concentration of the drug increasing, and when is it decreasing?
​

Accepted Answer

A)  Increasing on   , decreasing on   
B)  Increasing on   , decreasing on   
C)  Increasing on   , decreasing on   
D)  Increasing on   , decreasing on   
E)  Increasing on   , decreasing on   
A)  Increasing on   , decreasing on   
B)  Increasing on   , decreasing on   
C)  Increasing on   , decreasing on   
D)  Increasing on   , decreasing on   
E)  Increasing on   , decreasing on

Question 3

Find the absolute maximum value and the absolute minimum value, if any, of the given function. ​   on   ​

Accepted Answer

A)  Absolute maximum value: 75; absolute minimum value: - 134 
B)  Absolute maximum value: 26; absolute minimum value: - 134 
C)  Absolute maximum value: 26; absolute minimum value: - 6 
D)  Absolute maximum value: 75; absolute minimum value: - 6 
E)  No absolute extrema 
A)  Absolute maximum value: 75; absolute minimum value: - 134 
B)  Absolute maximum value: 26; absolute minimum value: - 134 
C)  Absolute maximum value: 26; absolute minimum value: - 6 
D)  Absolute maximum value: 75; absolute minimum value: - 6 
E)  No absolute extrema

Question 4

Find the horizontal and vertical asymptotes of the graph of the function. (You need not sketch the graph.)
​   ​
Horizontal asymptote(s) __________
​
Vertical asymptote(s) __________

Accepted Answer

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

Question 5

Determine the relative maxima and relative minima, if any. ​   ​

Accepted Answer

A)  Relative maximum: f(0) = 5; Relative minima: f(5) = 0 and f( - 5) = 0 
B)  Relative maximum: f(0) = 5; No relative minima 
C)  No relative maxima; Relative minimum: f(5) = 0 and f( - 5) = 0 
D)  No relative maxima or minima 
A)  Relative maximum: f(0) = 5; Relative minima: f(5) = 0 and f( - 5) = 0 
B)  Relative maximum: f(0) = 5; No relative minima 
C)  No relative maxima; Relative minimum: f(5) = 0 and f( - 5) = 0 
D)  No relative maxima or minima

Question 6

Phillip, the proprietor of a vineyard, estimates that the first 10,000 bottles of wine produced this season will fetch a profit of $2/bottle. However, the profit from each bottle beyond 10,000 drops by $0.0002 for each additional bottle sold. Assuming at least 10,000 bottles of wine are produced and sold, what is the maximum profit? Round the answer to two decimal places.
​
The maximum profit is $__________
​
What would be the price/bottle in this case? Round the answer to the nearest cent.
​
$__________/bottle

Accepted Answer

The answer of Phillip, the proprietor of a vineyard, estimates...

Question 7

A stone is thrown straight up from the roof of an 48-ft building. The distance (in feet) of the stone from the ground at any time t (in seconds) is given by   . ​Sketch the graph of h. When is the stone rising, and when is it falling? If the stone were to miss the building, when would it hit the ground?
​

Accepted Answer

A)  ​   Rising in the time interval (0, 1); falling in the time interval (1, 3); when t = 3 sec 
B)  ​   Rising in the time interval (0, 1); falling in the time interval (1, 3); when t = 3 sec 
C)  ​   Rising in the time interval (3, -1); falling in the time interval (-1, 1); when t = 1 sec 
A)  ​   Rising in the time interval (0, 1); falling in the time interval (1, 3); when t = 3 sec 
B)  ​   Rising in the time interval (0, 1); falling in the time interval (1, 3); when t = 3 sec 
C)  ​   Rising in the time interval (3, -1); falling in the time interval (-1, 1); when t = 1 sec

Question 8

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable. ​   ​

Accepted Answer

A)  Relative minimum:   
B)  Relative maximum:   
C)  Relative minimum:   
D)  Relative maximum:   
E)  none 
A)  Relative minimum:   
B)  Relative maximum:   
C)  Relative minimum:   
D)  Relative maximum:   
E)  none

Question 9

Find the inflection points, if any, of the following function. Otherwise, answer no solution.
​

Accepted Answer

The answer of Find the inflection points, if any, of...

Question 10

Find the inflection points of the following function. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

A manufacturer of tennis rackets finds that the total cost   (in dollars) of manufacturing   rackets/day is given by   . Each racket can be sold at a price of   dollars, where   is related to   by the demand equation   .
​
If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer.
​
__________ rackets/day

Accepted Answer

The answer of A manufacturer of tennis rackets finds that...

Question 12

Find the relative maxima and relative minima, if any, of the function. ​   ​

Accepted Answer

A)  Relative maximum:   ; No relative minima 
B)  No relative maxima; Relative minima   
C)  Relative maximum:   ; Relative minimum   
D)  No relative maxima or minima 
A)  Relative maximum:   ; No relative minima 
B)  No relative maxima; Relative minima   
C)  Relative maximum:   ; Relative minimum   
D)  No relative maxima or minima

Question 13

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

Accepted Answer

A)  Horizontal asymptote:   ; vertical asymptote   
B)  Vertical asymptote:   
C)  Horizontal asymptote:   
D)  Horizontal asymptotes:   and   
A)  Horizontal asymptote:   ; vertical asymptote   
B)  Vertical asymptote:   
C)  Horizontal asymptote:   
D)  Horizontal asymptotes:   and

Question 14

An apple orchard has an average yield of 36 bushels of apples/tree if tree density is 24 trees/acre. For each unit increase in tree density, the yield decreases by 3 bushels. How many trees should be planted in order to maximize the yield?
​
__________ trees

Accepted Answer

The answer of An apple orchard has an average yield...

Question 15

The graph of the function f shown in the accompanying figure gives the elevation of that part of the Boston Marathon course that includes the notorious Heartbreak Hill. Determine the intervals (stretches of the course) where the function f is increasing (the runner is laboring), where it is constant (the runner is taking a breather), and where it is decreasing (the runner is coasting). ​   ​

Accepted Answer

A)  Decreasing on   and   , increasing on   and   , and constant on   and   
B)  Decreasing on   and   , increasing on   and   , and constant on   and   
C)  Decreasing on   and   , increasing on   and   , and constant on   and   
A)  Decreasing on   and   , increasing on   and   , and constant on   and   
B)  Decreasing on   and   , increasing on   and   , and constant on   and   
C)  Decreasing on   and   , increasing on   and   , and constant on   and

Question 16

Determine where the function is concave upward. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 17

Find the relative maxima and relative minima, if any, of the function. ​   ​

Accepted Answer

A)  Relative minimum:   
B)  Relative minimum:   
C)  Relative maximum:   
D)  Relative maximum:   
E)  Relative minimum:   
A)  Relative minimum:   
B)  Relative minimum:   
C)  Relative maximum:   
D)  Relative maximum:   
E)  Relative minimum:

Question 18

The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, manufactured by Phonola Record Industries, is related to the price/compact disc. The equation     , where   denotes the unit price in dollars and   is the number of discs demanded, relates the demand to the price.
​
The total monthly cost (in dollars) for pressing and packaging   copies of this classical recording is given by     .
​
To maximize its profits, how many copies should Phonola produce each month?

Accepted Answer

The answer of The quantity demanded each month of the...

Question 19

Find the interval(s) where each function is increasing and the interval(s) where it is decreasing. ​   ​

Accepted Answer

A)  Increasing on   , decreasing on   
B)  Increasing on   and   , decreasing on   
C)  Increasing on   , decreasing on   
D)  Increasing on   and   
A)  Increasing on   , decreasing on   
B)  Increasing on   and   , decreasing on   
C)  Increasing on   , decreasing on   
D)  Increasing on   and

Question 20

The total worldwide box-office receipts for a long-running movie are approximated by the function ​   ​
Where   is measured in millions of dollars and x is the number of years since the movie's release.
​
Select the graph of the function T.
​

Accepted Answer

A)  ​ ​ ​   ​ 
B)  ​   ​ 
C)  ​   
D)  ​   ​ 
A)  ​ ​ ​   ​ 
B)  ​   ​ 
C)  ​   
D)  ​   ​

Find the relative maxima and relative minima, if any, of the function. Otherwise, answer none. Relative minima: Relative maxima:

The concentration (in milligrams/cubic centimeter) of a certain drug in a patient's body t hr after injection is given by . When is the concentration of the drug increasing, and when is it decreasing?

Find the absolute maximum value and the absolute minimum value, if any, of the given function. on

Find the horizontal and vertical asymptotes of the graph of the function. (You need not sketch the graph.) Horizontal asymptote(s) Vertical asymptote(s)

Determine the relative maxima and relative minima, if any.

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable.

Find the inflection points, if any, of the following function. Otherwise, answer no solution.

Find the inflection points of the following function.

Find the relative maxima and relative minima, if any, of the function.

Find the horizontal and vertical asymptotes of the graph.

An apple orchard has an average yield of 36 bushels of apples/tree if tree density is 24 trees/acre. For each unit increase in tree density, the yield decreases by 3 bushels. How many trees should be planted in order to maximize the yield? __________ trees

Determine where the function is concave upward.

Find the relative maxima and relative minima, if any, of the function.

Find the interval(s) where each function is increasing and the interval(s) where it is decreasing.

The total worldwide box-office receipts for a long-running movie are approximated by the function Where is measured in millions of dollars and x is the number of years since the movie's release. Select the graph of the function T.

Preliminaries

Functions, Limits, and the Derivative

Differentiation

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Probability and Calculus

Taylor Polynomials and Infinite Series

Trigonometric Functions

Filters

Exam 4: Applications of the Derivative

Find the relative maxima and relative minima, if any, of the function. Otherwise, answer none. ​ ​ Relative minima: __________ ​ Relative maxima: __________

The concentration (in milligrams/cubic centimeter) of a certain drug in a patient's body t hr after injection is given by ​ . ​ When is the concentration of the drug increasing, and when is it decreasing? ​

Find the absolute maximum value and the absolute minimum value, if any, of the given function. ​ on ​

Find the horizontal and vertical asymptotes of the graph of the function. (You need not sketch the graph.) ​ ​ Horizontal asymptote(s) __________ ​ Vertical asymptote(s) __________

Determine the relative maxima and relative minima, if any. ​ ​

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable. ​ ​

Find the inflection points, if any, of the following function. Otherwise, answer no solution. ​

Find the inflection points of the following function. ​ ​

Find the relative maxima and relative minima, if any, of the function. ​ ​

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

An apple orchard has an average yield of 36 bushels of apples/tree if tree density is 24 trees/acre. For each unit increase in tree density, the yield decreases by 3 bushels. How many trees should be planted in order to maximize the yield? ​ __________ trees

Determine where the function is concave upward. ​ ​

Find the relative maxima and relative minima, if any, of the function. ​ ​

Find the interval(s) where each function is increasing and the interval(s) where it is decreasing. ​ ​

The total worldwide box-office receipts for a long-running movie are approximated by the function ​ ​ Where is measured in millions of dollars and x is the number of years since the movie's release. ​ Select the graph of the function T. ​

Preliminaries

Functions, Limits, and the Derivative

Differentiation

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Probability and Calculus

Taylor Polynomials and Infinite Series

Trigonometric Functions

Filters

Find the relative maxima and relative minima, if any, of the function. Otherwise, answer none. Relative minima: Relative maxima:

The concentration (in milligrams/cubic centimeter) of a certain drug in a patient's body t hr after injection is given by . When is the concentration of the drug increasing, and when is it decreasing?

Find the absolute maximum value and the absolute minimum value, if any, of the given function. on

Find the horizontal and vertical asymptotes of the graph of the function. (You need not sketch the graph.) Horizontal asymptote(s) Vertical asymptote(s)

Determine the relative maxima and relative minima, if any.

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable.

Find the inflection points, if any, of the following function. Otherwise, answer no solution.

Find the inflection points of the following function.

Find the relative maxima and relative minima, if any, of the function.

Find the horizontal and vertical asymptotes of the graph.

An apple orchard has an average yield of 36 bushels of apples/tree if tree density is 24 trees/acre. For each unit increase in tree density, the yield decreases by 3 bushels. How many trees should be planted in order to maximize the yield? __________ trees

Determine where the function is concave upward.

Find the relative maxima and relative minima, if any, of the function.

Find the interval(s) where each function is increasing and the interval(s) where it is decreasing.

The total worldwide box-office receipts for a long-running movie are approximated by the function Where is measured in millions of dollars and x is the number of years since the movie's release. Select the graph of the function T.