Question 1

Find the inflection points, if any, of the function.

Accepted Answer

A)    
B)    
C)    
D) none 
A)    
B)    
C)    
D) none

Question 2

Determine whether the statement is true or false.If it is true, explain why it is true.If it is false, give an example to show why it is false.
If f is decreasing on (a, b), then   for each x in (a, b).

Accepted Answer

False.For

Question 3

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

Accepted Answer

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

Question 4

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

Question 5

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

Accepted Answer

A) Vertical asymptote: x = -4 
B) Vertical asymptotes: x = -4, x = -1 and x = 0 
C) Vertical asymptotes: x = -4 and x = -1; Horizontal asymptotes: y = 1 and y = -1 
D) Vertical asymptote: x = -4; Horizontal asymptotes: y = 0 
A) Vertical asymptote: x = -4 
B) Vertical asymptotes: x = -4, x = -1 and x = 0 
C) Vertical asymptotes: x = -4 and x = -1; Horizontal asymptotes: y = 1 and y = -1 
D) Vertical asymptote: x = -4; Horizontal asymptotes: y = 0

Question 6

If the graph of f is concave upward on (a, b), then the graph of - f is concave upward on (a, b).

Accepted Answer

A) True 
 B)False

Question 7

Suppose the total cost function for manufacturing a certain product is   dollars, where x represents the number of units produced.Find the level of production that will minimize the average cost.Round the answer to the nearest integer.

Accepted Answer

A) 46 units 
B) 50 units 
C) 40 units 
D) 44 units 
A) 46 units 
B) 50 units 
C) 40 units 
D) 44 units

Question 8

Find the inflection points, if any, of the function.

Accepted Answer

A) (1, - 11) 
B) (0, - 22) 
C) (8, - 11) 
D) none 
A) (1, - 11) 
B) (0, - 22) 
C) (8, - 11) 
D) none

Question 9

What are the dimensions of a closed rectangular box that has a square cross section, a capacity of   and is constructed using the least amount of material? Round the answer to two decimal places.

Accepted Answer

The answer of What are the dimensions of a closed...

Question 10

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

Accepted Answer

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

Question 11

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 12

The owner of the Rancho Los Feliz has 3,000 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

The answer of The owner of the Rancho Los Feliz...

Question 13

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

Accepted Answer

A) Decreasing on (0, 2.5) 
B) Increasing on (0, 1) and decreasing on (1, 5) 
C) Increasing on (0, 10) 
D) The concentration of the drug is constant. 
A) Decreasing on (0, 2.5) 
B) Increasing on (0, 1) and decreasing on (1, 5) 
C) Increasing on (0, 10) 
D) The concentration of the drug is constant.

Question 14

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

Accepted Answer

A) Relative minimum: f (- 1) = 17 
B) Relative maximum: f (- 2) = 12 
C) Relative maximum: f (- 1) = 17 
D) Relative minimum: f (- 2) = 12 
E) none 
A) Relative minimum: f (- 1) = 17 
B) Relative maximum: f (- 2) = 12 
C) Relative maximum: f (- 1) = 17 
D) Relative minimum: f (- 2) = 12 
E) none

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

The second derivative of g(x)

Question 17

The estimated monthly profit (in dollars) realizable by Cannon Precision Instruments for manufacturing and selling x units of its model M1 camera is   .
To maximize its profits, how many cameras should Cannon produce each month?
__________ cameras

Accepted Answer

The answer of The estimated monthly profit (in dollars) realizable...

Question 18

Find the absolute maximum value and the absolute minimum value, if any, of the given function.   on [1, 4]

Accepted Answer

A) Absolute maximum value:   ; Absolute minimum value: 5 
B) Absolute maximum value:   ; Absolute minimum value: 4 
C) Absolute maximum value:   ; Absolute minimum value: 5 
D) Absolute maximum value:   ; Absolute minimum value: 4 
E) Absolute maximum value:   ; Absolute minimum value:
  
A) Absolute maximum value:   ; Absolute minimum value: 5 
B) Absolute maximum value:   ; Absolute minimum value: 4 
C) Absolute maximum value:   ; Absolute minimum value: 5 
D) Absolute maximum value:   ; Absolute minimum value: 4 
E) Absolute maximum value:   ; Absolute minimum value:

Question 19

Find the relative maxima and relative minima of the function.

Accepted Answer

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

Question 20

Determine where the function is concave upward.

Accepted Answer

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

Find the inflection points, if any, of the function.

Determine whether the statement is true or false.If it is true, explain why it is true.If it is false, give an example to show why it is false. If f is decreasing on (a, b), then for each x in (a, b).

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

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?

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

If the graph of f is concave upward on (a, b), then the graph of - f is concave upward on (a, b).

Suppose the total cost function for manufacturing a certain product is dollars, where x represents the number of units produced.Find the level of production that will minimize the average cost.Round the answer to the nearest integer.

Find the inflection points, if any, of the function.

What are the dimensions of a closed rectangular box that has a square cross section, a capacity of and is constructed using the least amount of material? Round the answer to two decimal places.

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

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

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

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

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

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

The estimated monthly profit (in dollars) realizable by Cannon Precision Instruments for manufacturing and selling x units of its model M1 camera is . To maximize its profits, how many cameras should Cannon produce each month? __________ cameras

Find the absolute maximum value and the absolute minimum value, if any, of the given function. on [1, 4]

Find the relative maxima and relative minima of the function.

Determine where the function is concave upward.

Preliminaries

Functions, Limits and the Derivative

Differentiation

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

Exam 4: Applications of the Derivative

Find the inflection points, if any, of the function.

Determine whether the statement is true or false.If it is true, explain why it is true.If it is false, give an example to show why it is false. If f is decreasing on (a, b), then for each x in (a, b).

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

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?

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

If the graph of f is concave upward on (a, b), then the graph of - f is concave upward on (a, b).

Suppose the total cost function for manufacturing a certain product is dollars, where x represents the number of units produced.Find the level of production that will minimize the average cost.Round the answer to the nearest integer.

Find the inflection points, if any, of the function.

What are the dimensions of a closed rectangular box that has a square cross section, a capacity of and is constructed using the least amount of material? Round the answer to two decimal places.

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

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

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

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

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

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

The estimated monthly profit (in dollars) realizable by Cannon Precision Instruments for manufacturing and selling x units of its model M1 camera is . To maximize its profits, how many cameras should Cannon produce each month? __________ cameras

Find the absolute maximum value and the absolute minimum value, if any, of the given function. on [1, 4]

Find the relative maxima and relative minima of the function.

Determine where the function is concave upward.

Preliminaries

Functions, Limits and the Derivative

Differentiation

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters