Question 1

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

Accepted Answer

A)  Absolute maximum value: none; absolute minimum value: 0 
B)  Absolute maximum value: 0; absolute minimum value: -8 
C)  Absolute maximum value: 8; absolute minimum value: 0 
D)  No absolute extrema 
A)  Absolute maximum value: none; absolute minimum value: 0 
B)  Absolute maximum value: 0; absolute minimum value: -8 
C)  Absolute maximum value: 8; absolute minimum value: 0 
D)  No absolute extrema D

Question 2

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

Accepted Answer

A)  Vertical asymptote:   ; Horizontal asymptote:   
B)  Vertical asymptote:   ; Horizontal asymptote:   
C)  Vertical asymptote:   ; Horizontal asymptote:   
D)  Vertical asymptote:   ; Horizontal asymptote:   
A)  Vertical asymptote:   ; Horizontal asymptote:   
B)  Vertical asymptote:   ; Horizontal asymptote:   
C)  Vertical asymptote:   ; Horizontal asymptote:   
D)  Vertical asymptote:   ; Horizontal asymptote:   D

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

A)  Relative maximum: f (1) = 6 
B)  Relative maximum: f (0) = 2 
C)  Relative minimum: f (0) = 2 
D)  Relative minimum: f (1) = 6 
E)  none 
A)  Relative maximum: f (1) = 6 
B)  Relative maximum: f (0) = 2 
C)  Relative minimum: f (0) = 2 
D)  Relative minimum: f (1) = 6 
E)  none

Question 5

In the diagram, S represents the position of a power relay station located on a straight coast, and E shows the location of a marine biology experimental station on an island. A cable is to be laid connecting the relay station with the experimental station. ​   ​
If the cost of running the cable on land is $2.00/running foot and the cost of running the cable under water is $5.20/running foot, locate the point P that will result in a minimum cost (solve for x).
​

Accepted Answer

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

Question 6

Determine where the function is concave upward and where it is concave downward. ​   ​

Accepted Answer

A)  concave upward on   ; concave downward on   
B)  concave upward on   ; concave downward on   
C)  concave upward on   ; concave downward on   
D)  concave upward on   ; concave downward on   
E)  concave upward on   ; concave downward on   
A)  concave upward on   ; concave downward on   
B)  concave upward on   ; concave downward on   
C)  concave upward on   ; concave downward on   
D)  concave upward on   ; concave downward on   
E)  concave upward on   ; concave downward on

Question 7

The owner of the Rancho Los Feliz has 3,200 yd of fencing material with which to enclose a rectangular piece of grazing land along the straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area that he can enclose? What is this area? ​

Accepted Answer

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

Question 8

Find the graph of the derivative of the function. ​   ​

Accepted Answer

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

Question 9

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 8 in. long and 3 in. wide, find the dimensions of the box that will yield the maximum volume. ​

Accepted Answer

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

Question 10

Select the graph of the function using the curve-sketching guide. ​   ​

Accepted Answer

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

Question 11

Determine where the function is concave downward. ​   ​

Accepted Answer

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

Question 12

The total annual revenue R of the Miramar Resorts Hotel is related to the amount of money x the hotel spends on advertising its services by the function ​   where both R and x are measured in thousands of dollars.
​Use this function to:
​1) Find the interval where the graph of R is concave upward and the interval where the graph of R is concave downward.
2) Find the inflection point of R.
3) Determine if it would it be more beneficial for the hotel to increase its advertising budget slightly when the budget is $240,000 or when it is $260,000.

Accepted Answer

A)  concave downward on   ; concave upward on   ; inflection point is   
B)  concave upward on   ; concave downward on   ; inflection point is   
C)  concave upward on   ; concave downward on   ; inflection point is   
D)  concave downward on   ; concave upward on   ; inflection point is   
E)  concave upward on   ; concave downward on   ; inflection point is   
A)  concave downward on   ; concave upward on   ; inflection point is   
B)  concave upward on   ; concave downward on   ; inflection point is   
C)  concave upward on   ; concave downward on   ; inflection point is   
D)  concave downward on   ; concave upward on   ; inflection point is   
E)  concave upward on   ; concave downward on   ; inflection point is

Question 13

You are given the graph of some function f defined on the indicated interval. Find the absolute maximum and the absolute minimum of f, if they exist. ​   ​
F defined on   ​

Accepted Answer

A)  Absolute maximum value: 0.3; absolute minimum value: -6 
B)  Absolute maximum value: 0.3; absolute minimum value: -2 
C)  Absolute maximum value: -2; absolute minimum value: -6 
D)  Absolute maximum value: 0.3; absolute minimum value: 0 
A)  Absolute maximum value: 0.3; absolute minimum value: -6 
B)  Absolute maximum value: 0.3; absolute minimum value: -2 
C)  Absolute maximum value: -2; absolute minimum value: -6 
D)  Absolute maximum value: 0.3; absolute minimum value: 0

Question 14

Show that the function   is concave upward wherever it is defined. ​

Accepted Answer

A)  The function   is defined for any value of x and   hence the function is concave upward for any x. 
B)  The second derivative of   is   . It is positive for any value of x, hence the function is concave upward for any x. 
C)  The first derivative of   is   . It is positive for any value of x, hence the function is concave upward for any x. 
A)  The function   is defined for any value of x and   hence the function is concave upward for any x. 
B)  The second derivative of   is   . It is positive for any value of x, hence the function is concave upward for any x. 
C)  The first derivative of   is   . It is positive for any value of x, hence the function is concave upward for any x.

Question 15

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

Accepted Answer

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

Question 16

You are given the graph of a function
Determine the intervals where f is concave downward. ​   ​

Accepted Answer

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

Question 17

Determine where the function is concave downward. ​   ​

Accepted Answer

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

Question 18

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 19

The quantity demanded each month of the Sicard wristwatch is related to the unit price by the equation     , where   is measured in dollars and   is measured in units of a thousand.
To yield a maximum revenue, how many watches must be sold?
​  __________

Accepted Answer

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

Question 20

A division of Chapman Corporation manufactures a pager. The weekly fixed cost for the division is $20,000, and the variable cost for producing   pagers/week is   dollars. The company realizes a revenue of     dollars from the sale of   pagers/week.
Find the level of production that will yield a maximum profit for the manufacturer.

Accepted Answer

The answer of A division of Chapman Corporation manufactures a...

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.

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

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

Determine where the function is concave upward and where it is concave downward.

The owner of the Rancho Los Feliz has 3,200 yd of fencing material with which to enclose a rectangular piece of grazing land along the straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area that he can enclose? What is this area?

Find the graph of the derivative of the function.

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 8 in. long and 3 in. wide, find the dimensions of the box that will yield the maximum volume.

Select the graph of the function using the curve-sketching guide.

Determine where the function is concave downward.

You are given the graph of some function f defined on the indicated interval. Find the absolute maximum and the absolute minimum of f, if they exist. F defined on

Show that the function is concave upward wherever it is defined.

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

You are given the graph of a function Determine the intervals where f is concave downward.

Determine where the function is concave downward.

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

The quantity demanded each month of the Sicard wristwatch is related to the unit price by the equation , where is measured in dollars and is measured in units of a thousand. To yield a maximum revenue, how many watches must be sold? __________

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 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. ​ ​

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

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

Determine where the function is concave upward and where it is concave downward. ​ ​

The owner of the Rancho Los Feliz has 3,200 yd of fencing material with which to enclose a rectangular piece of grazing land along the straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area that he can enclose? What is this area? ​

Find the graph of the derivative of the function. ​ ​

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 8 in. long and 3 in. wide, find the dimensions of the box that will yield the maximum volume. ​

Select the graph of the function using the curve-sketching guide. ​ ​

Determine where the function is concave downward. ​ ​

You are given the graph of some function f defined on the indicated interval. Find the absolute maximum and the absolute minimum of f, if they exist. ​ ​ F defined on ​

Show that the function is concave upward wherever it is defined. ​

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

You are given the graph of a function Determine the intervals where f is concave downward. ​ ​

Determine where the function is concave downward. ​ ​

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

The quantity demanded each month of the Sicard wristwatch is related to the unit price by the equation , where is measured in dollars and is measured in units of a thousand. To yield a maximum revenue, how many watches must be sold? ​ __________

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 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.

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

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

Determine where the function is concave upward and where it is concave downward.

The owner of the Rancho Los Feliz has 3,200 yd of fencing material with which to enclose a rectangular piece of grazing land along the straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area that he can enclose? What is this area?

Find the graph of the derivative of the function.

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 8 in. long and 3 in. wide, find the dimensions of the box that will yield the maximum volume.

Select the graph of the function using the curve-sketching guide.

Determine where the function is concave downward.

You are given the graph of some function f defined on the indicated interval. Find the absolute maximum and the absolute minimum of f, if they exist. F defined on

Show that the function is concave upward wherever it is defined.

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

You are given the graph of a function Determine the intervals where f is concave downward.

Determine where the function is concave downward.

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

The quantity demanded each month of the Sicard wristwatch is related to the unit price by the equation , where is measured in dollars and is measured in units of a thousand. To yield a maximum revenue, how many watches must be sold? __________