Question 1

Use the graph of the function   given below to estimate the open intervals on which the function is increasing or 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   B

Question 2

For the function   : (a) Find the critical numbers of f (if any);
(b) Find the open intervals where the function is increasing or decreasing; and
(c) Apply the First Derivative Test to identify all relative extrema.
Use a graphing utility to confirm your results.

Accepted Answer

A)  (a)  
(b) increasing:   ; decreasing:  
(c) relative max:   
B)  (a)  
(b) increasing:   ; decreasing:  
(c) relative max:   
C)  (a)  
(b) decreasing:   ; increasing:  
(c) relative min:   
D)  (a)  
(b) decreasing:   ; increasing:  
(c) relative min:   ; relative max:   
E)  (a)  
(b) decreasing:   ; increasing:  
(c) relative min:   
A)  (a)  
(b) increasing:   ; decreasing:  
(c) relative max:   
B)  (a)  
(b) increasing:   ; decreasing:  
(c) relative max:   
C)  (a)  
(b) decreasing:   ; increasing:  
(c) relative min:   
D)  (a)  
(b) decreasing:   ; increasing:  
(c) relative min:   ; relative max:   
E)  (a)  
(b) decreasing:   ; increasing:  
(c) relative min:   C

Question 3

The resistance R of a certain type of resistor is   where R is measured in ohms and the temperature T is measured in degrees Celsius. Use a computer algebra system to find

Accepted Answer

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

Question 4

For the function   : (a) Find the critical numbers of f (if any);
(b) Find the open intervals where the function is increasing or decreasing; and
(c) Apply the First Derivative Test to identify all relative extrema.
Then use a graphing utility to confirm your results.

Accepted Answer

A)  (a) x = 0 ,  
(b) increasing:   ; decreasing:  
(c) relative max:   ; relative min:   
B)  (a) x = 0 ,  
(b) decreasing:   ; increasing:  
(c) relative min:   ; relative max:   
C)  (a) x = 0 ,  
(b) increasing:   ; decreasing:  
(c) relative max:   ; no relative min. 
D)  (a) x = 0 ,  
(b) increasing:   ; decreasing:  
(c) relative max:   ; relative min:   
E)  (a) x = 0 ,  
(b) decreasing:   ; increasing:  
(c) relative min:   ; relative max:   
A)  (a) x = 0 ,  
(b) increasing:   ; decreasing:  
(c) relative max:   ; relative min:   
B)  (a) x = 0 ,  
(b) decreasing:   ; increasing:  
(c) relative min:   ; relative max:   
C)  (a) x = 0 ,  
(b) increasing:   ; decreasing:  
(c) relative max:   ; no relative min. 
D)  (a) x = 0 ,  
(b) increasing:   ; decreasing:  
(c) relative max:   ; relative min:   
E)  (a) x = 0 ,  
(b) decreasing:   ; increasing:  
(c) relative min:   ; relative max:

Question 5

Identify the open intervals where the function   is increasing or decreasing.

Accepted Answer

A)  decreasing:   ; increasing:   
B)  decreasing on   
C)  increasing:   ; decreasing:   
D)  increasing:   ; decreasing:   
E)  increasing:   ; decreasing:   
A)  decreasing:   ; increasing:   
B)  decreasing on   
C)  increasing:   ; decreasing:   
D)  increasing:   ; decreasing:   
E)  increasing:   ; decreasing:

Question 6

Find the open interval(s) on which   is increasing or 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 7

The resistance R of a certain type of resistor is   where R is measured in ohms and the temperature T is measured in degrees Celsius. Use a computer algebra system to find the critical number of the function. Round numerical values in your answer to the nearest whole number.

Accepted Answer

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

Question 8

A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is   radians. The distance (in meters) the ball bearing rolls in t seconds is   . Determine the speed of the ball bearing after t seconds.

Accepted Answer

A)  speed:   meters per second 
B)  speed:   meters per second 
C)  speed:   meters per second 
D)  speed:   meters per second 
E)  speed:   meters per second 
A)  speed:   meters per second 
B)  speed:   meters per second 
C)  speed:   meters per second 
D)  speed:   meters per second 
E)  speed:   meters per second

Question 9

A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is   radians. The distance (in meters) the ball bearing rolls in t seconds is   . Determine the value of   after one second. Round numerical values in your answer to one decimal place.

Accepted Answer

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

Question 10

Find the relative maxima of   on the interval   by applying the First Derivative Test. Round numerical values in your answer to three decimal places.

Accepted Answer

A)  relative maxima:   
B)  relative maxima:   
C)  relative maxima:   
D)  relative maxima:   
E)  relative maxima:   
A)  relative maxima:   
B)  relative maxima:   
C)  relative maxima:   
D)  relative maxima:   
E)  relative maxima:

Question 11

Find the open interval(s) on which the function   is increasing in the interval   Round numerical values in your answer to three decimal places.

Accepted Answer

A)  increasing on:   
B)  increasing on:   
C)  increasing on:   
D)  increasing on:   
E)  increasing on:   
A)  increasing on:   
B)  increasing on:   
C)  increasing on:   
D)  increasing on:   
E)  increasing on:

Question 12

Find the relative extremum of   by applying the First Derivative Test.

Accepted Answer

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

Question 13

Identify the open intervals on which the function   is increasing or 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 14

Find the critical number of the function   .

Accepted Answer

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

Question 15

Find the open interval(s) on which the function   is increasing in the interval   Round numerical values in your answer to three decimal places.

Accepted Answer

A)  increasing on:   
B)  increasing on:   
C)  increasing on:   
D)  increasing on:   
E)  increasing on:   
A)  increasing on:   
B)  increasing on:   
C)  increasing on:   
D)  increasing on:   
E)  increasing on:

Question 16

Find the relative minima of   on the interval   by applying the First Derivative Test. Round numerical values in your answer to three decimal places.

Accepted Answer

A)  relative minima:   
B)  relative minima:   
C)  relative minima:   
D)  relative minima:   
E)  relative minima:   
A)  relative minima:   
B)  relative minima:   
C)  relative minima:   
D)  relative minima:   
E)  relative minima:

Question 17

Identify the open intervals where the function   is increasing or decreasing.

Accepted Answer

A)  decreasing on   
B)  increasing on   
C)    
D)  decreasing on   ; increasing on   
E)    
A)  decreasing on   
B)  increasing on   
C)    
D)  decreasing on   ; increasing on   
E)

Exam 4: Section 3: Applications of Differentiation

Use the graph of the function given below to estimate the open intervals on which the function is increasing or decreasing.

For the function : (a) Find the critical numbers of f (if any); (b) Find the open intervals where the function is increasing or decreasing; and (c) Apply the First Derivative Test to identify all relative extrema. Use a graphing utility to confirm your results.

The resistance R of a certain type of resistor is where R is measured in ohms and the temperature T is measured in degrees Celsius. Use a computer algebra system to find

For the function : (a) Find the critical numbers of f (if any); (b) Find the open intervals where the function is increasing or decreasing; and (c) Apply the First Derivative Test to identify all relative extrema. Then use a graphing utility to confirm your results.

Identify the open intervals where the function is increasing or decreasing.

Find the open interval(s) on which is increasing or decreasing.

The resistance R of a certain type of resistor is where R is measured in ohms and the temperature T is measured in degrees Celsius. Use a computer algebra system to find the critical number of the function. Round numerical values in your answer to the nearest whole number.

A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is radians. The distance (in meters) the ball bearing rolls in t seconds is . Determine the speed of the ball bearing after t seconds.

A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is radians. The distance (in meters) the ball bearing rolls in t seconds is . Determine the value of after one second. Round numerical values in your answer to one decimal place.

Find the relative maxima of on the interval by applying the First Derivative Test. Round numerical values in your answer to three decimal places.

Find the open interval(s) on which the function is increasing in the interval Round numerical values in your answer to three decimal places.

Find the relative extremum of by applying the First Derivative Test.

Identify the open intervals on which the function is increasing or decreasing.

Find the critical number of the function .

Find the open interval(s) on which the function is increasing in the interval Round numerical values in your answer to three decimal places.

Find the relative minima of on the interval by applying the First Derivative Test. Round numerical values in your answer to three decimal places.

Identify the open intervals where the function is increasing or decreasing.

Section 1: Preparation for Calculus

Section 2: Preparation for Calculus

Section 3: Preparation for Calculus

Section 4: Preparation for Calculus

Section 5: Preparation for Calculus

Section 6: Preparation for Calculus

Section 1: Limits and Their Properties

Section 2: Limits and Their Properties

Section 3: Limits and Their Properties

Section 4: Limits and Their Properties

Section 5 : Limits and Their Properties

Section 1 : Differentiation

Section 2: Differentiation

Section 3: Differentiation

Section 4 : Differentiation

Section 5: Differentiation

Section 6: Differentiation

Section 7: Differentiation

Section 8: Differentiation

Section 1 : Applications of Differentiation

Section 2: Applications of Differentiation

Section 4: Applications of Differentiation

Section 5: Applications of Differentiation

Section 6: Applications of Differentiation

Section 7: Applications of Differentiation

Section 8: Applications of Differentiation

Section 1: Integration

Section 2: Integration

Section 3: Integration

Section 4: Integration

Section 5: Integration

Section 6: Integration

Section 7: Integration

Section 8: Integration

Section 9: Integration

Section 1: Differential Equations

Section 2: Differential Equations

Section 3: Differential Equations

Section 4: Differential Equations

Section 5: Differential Equations

Section 1: Applications of Integration

Section 2: Applications of Integration

Section 3: Applications of Integration

Section 4: Applications of Integration

Section 5: Applications of Integration

Section 6: Applications of Integration

Section 7: Applications of Integration

Section 1: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 2: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 3: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 4: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 5: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 6: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 7: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 8: Integration Techniques, Lhôpitals Rule, and Improper Integrals

Section 1: Infinite Series

Section 2: Infinite Series

Section 3: Infinite Series

Section 4: Infinite Series

Section 5: Infinite Series

Section 6: Infinite Series

Section 7: Infinite Series