Question 1

Locate the absolute extrema of the function   on the closed interval   .

Accepted Answer

A)  absolute max: (0,1) ; absolute min:   
B)  absolute max:   ; absolute min: (0, 1) 
C)  absolute max:   ; no absolute min 
D)  no absolute max; absolute min: (0, 1) 
E)  absolute max: (0,1); no absolute min 
A)  absolute max: (0,1) ; absolute min:   
B)  absolute max:   ; absolute min: (0, 1) 
C)  absolute max:   ; no absolute min 
D)  no absolute max; absolute min: (0, 1) 
E)  absolute max: (0,1); no absolute min A

Question 2

Sketch the graph of the function   and locate the absolute extrema of the function on the interval   .

Accepted Answer

A)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum 
B)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum 
C)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum 
D)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum 
E)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum 
A)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum 
B)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum 
C)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum 
D)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum 
E)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum E

Question 3

Locate the absolute extrema of the given function on the closed interval   .

Accepted Answer

A)  absolute max: (0, 0); absolute min   
B)  absolute max:   ; absolute min (0, 0) 
C)  absolute max:   ; absolute min   
D)  absolute max:   ; no absolute min 
E)  no absolute max; absolute min:   
A)  absolute max: (0, 0); absolute min   
B)  absolute max:   ; absolute min (0, 0) 
C)  absolute max:   ; absolute min   
D)  absolute max:   ; no absolute min 
E)  no absolute max; absolute min:   C

Question 4

Locate the absolute extrema of the function   on the closed interval   .

Accepted Answer

A)  absolute maximum:  
Absolute minimum:   
B)  absolute maximum:  
Absolute minimum:   
C)  absolute maximum:  
Absolute minimum:   
D)  absolute maximum:  
Absolute minimum:   
E)  absolute maximum:  
Absolute minimum:   
A)  absolute maximum:  
Absolute minimum:   
B)  absolute maximum:  
Absolute minimum:   
C)  absolute maximum:  
Absolute minimum:   
D)  absolute maximum:  
Absolute minimum:   
E)  absolute maximum:  
Absolute minimum:

Question 5

Find the value of the derivative (if it exists) of the function   at the extremum point   .

Accepted Answer

A)    
B)  0 
C)    
D)    
E)  does not exist 
A)    
B)  0 
C)    
D)    
E)  does not exist

Question 6

Use a graphing utility to graph the function   and locate the absolute extrema of the function on the interval   .

Accepted Answer

A)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum
Critical points: none 
B)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum
Critical points: none 
C)  left endpoint:   absolute minimum
Right endpoint:  
Critical points:   absolute maximum 
D)  left endpoint:   absolute maximum
Right endpoint:   absolute minimum
Critical points: none 
E)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum
Critical points:   
A)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum
Critical points: none 
B)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum
Critical points: none 
C)  left endpoint:   absolute minimum
Right endpoint:  
Critical points:   absolute maximum 
D)  left endpoint:   absolute maximum
Right endpoint:   absolute minimum
Critical points: none 
E)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum
Critical points:

Question 7

Find all critical numbers of of the function   ,   .

Accepted Answer

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

Question 8

Locate the absolute extrema of the function   on the closed interval   .

Accepted Answer

A)  absolute max:   ; absolute min:   
B)  no absolute max; absolute min:   
C)  absolute max:   ; absolute min:   
D)  absolute max:   ; no absolute min 
E)  no absolute max or min 
A)  absolute max:   ; absolute min:   
B)  no absolute max; absolute min:   
C)  absolute max:   ; absolute min:   
D)  absolute max:   ; no absolute min 
E)  no absolute max or min

Question 9

Find the value of the derivative (if it exists) of the function   at the extremum point   .

Accepted Answer

A)    
B)    
C)    
D)  0 
E)  1 
A)    
B)    
C)    
D)  0 
E)  1

Question 10

Locate the absolute extrema of the function   on the closed interval   .

Accepted Answer

A)  absolute max:   ; no absolute min 
B)  no absolute max or min 
C)  no absolute max; absolute min:   
D)  absolute max:   ; absolute min:   
E)  absolute max:   ; absolute min:   
A)  absolute max:   ; no absolute min 
B)  no absolute max or min 
C)  no absolute max; absolute min:   
D)  absolute max:   ; absolute min:   
E)  absolute max:   ; absolute min:

Question 11

Use a computer algebra system to graph the function   and determine all absolute extrema on the interval   .

Accepted Answer

A)  absolute maximum:  
Absolute minimum:   
B)  absolute maximum:  
Absolute minimum:   
C)  absolute maximum:  
Absolute minimum:   
D)  absolute maximum:  
Absolute minimum:   
E)  absolute maximum:  
Absolute minimum:   
A)  absolute maximum:  
Absolute minimum:   
B)  absolute maximum:  
Absolute minimum:   
C)  absolute maximum:  
Absolute minimum:   
D)  absolute maximum:  
Absolute minimum:   
E)  absolute maximum:  
Absolute minimum:

Question 12

Locate the absolute extrema of the function   on the closed interval   .

Accepted Answer

A)  The absolute   is   , and it occurs at the left endpoint   .
The absolute   is   , and it occurs at the right endpoint   . 
B)  The absolute   is   , and it occurs at the right endpoint   .
The absolute   is   , and it occurs at the left endpoint   . 
C)  The absolute   is   , and it occurs at the left endpoint   .
The absolute   is   , and it occurs at the right endpoint   . 
D)  The absolute   is   , and it occurs at the right endpoint   .
The absolute   is   and it occurs at the left endpoint   . 
E)  The absolute   is   , and it occurs at the left endpoint   .
The absolute   is   , and it occurs at the right endpoint   . 
A)  The absolute   is   , and it occurs at the left endpoint   .
The absolute   is   , and it occurs at the right endpoint   . 
B)  The absolute   is   , and it occurs at the right endpoint   .
The absolute   is   , and it occurs at the left endpoint   . 
C)  The absolute   is   , and it occurs at the left endpoint   .
The absolute   is   , and it occurs at the right endpoint   . 
D)  The absolute   is   , and it occurs at the right endpoint   .
The absolute   is   and it occurs at the left endpoint   . 
E)  The absolute   is   , and it occurs at the left endpoint   .
The absolute   is   , and it occurs at the right endpoint   .

Question 13

Locate the absolute extrema of the function   on the closed interval   . Round your answers to four decimal places.

Accepted Answer

A)  left endpoint:  
Right endpoint:   absolute maximum
Critical points:   absolute minimum 
B)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum
Critical points: none 
C)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum
Critical points:   
D)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum
Critical points: none 
E)  left endpoint:  
Right endpoint:   absolute maximum
Critical points:   absolute minimum 
A)  left endpoint:  
Right endpoint:   absolute maximum
Critical points:   absolute minimum 
B)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum
Critical points: none 
C)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum
Critical points:   
D)  left endpoint:   absolute minimum
Right endpoint:   absolute maximum
Critical points: none 
E)  left endpoint:  
Right endpoint:   absolute maximum
Critical points:   absolute minimum

Question 14

Use a graphing utility to graph the function   and locate the absolute extrema of the function on the interval   .

Accepted Answer

A)  absolute minimum:  
No absolute maximum 
B)  absolute minimum:  
No absolute maximum 
C)  absolute minimum:  
No absolute maximum 
D)  absolute minimum:  
Absolute maximum:   
E)  absolute maximum:  
Absolute minimum:   
A)  absolute minimum:  
No absolute maximum 
B)  absolute minimum:  
No absolute maximum 
C)  absolute minimum:  
No absolute maximum 
D)  absolute minimum:  
Absolute maximum:   
E)  absolute maximum:  
Absolute minimum:

Question 15

Find all critical numbers of the function   .

Accepted Answer

A)  critical numbers:   
B)  critical numbers:   
C)  critical numbers:   
D)  critical numbers:   
E)  no critical numbers 
A)  critical numbers:   
B)  critical numbers:   
C)  critical numbers:   
D)  critical numbers:   
E)  no critical numbers

Question 16

Find the value of the derivative (if it exists) of   at the indicated extremum.

Accepted Answer

A)    is undefined. 
B)    
C)    
D)    
E)    
A)    is undefined. 
B)    
C)    
D)    
E)

Question 17

Locate the absolute extrema of the function   on the closed interval   .

Accepted Answer

A)  The absolute maximum is   , and it occurs at the critical number x = 0.
The absolute minimum is   , and it occurs at the left endpoint   . 
B)  The absolute maximum is   , and it occurs at either endpoint   .
The absolute minimum is 0, and it occurs at the critical number x = 0. 
C)  The absolute maximum is   , and it occurs only at the left endpoint   .
The absolute minimum is 0 and it occurs at the critical number x = 0. 
D)  The absolute maximum is   , and it occurs at the critical number x = 0.
The absolute minimum is   , and it occurs at the right endpoint   . 
E)  The absolute maximum is   , and it occurs only at the right endpoint  
The absolute minimum is 0 and it occurs at the critical number x = 0. 
A)  The absolute maximum is   , and it occurs at the critical number x = 0.
The absolute minimum is   , and it occurs at the left endpoint   . 
B)  The absolute maximum is   , and it occurs at either endpoint   .
The absolute minimum is 0, and it occurs at the critical number x = 0. 
C)  The absolute maximum is   , and it occurs only at the left endpoint   .
The absolute minimum is 0 and it occurs at the critical number x = 0. 
D)  The absolute maximum is   , and it occurs at the critical number x = 0.
The absolute minimum is   , and it occurs at the right endpoint   . 
E)  The absolute maximum is   , and it occurs only at the right endpoint  
The absolute minimum is 0 and it occurs at the critical number x = 0.

Question 18

Find all critical numbers of the function   ,   .

Accepted Answer

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

Question 19

Find any critical numbers of the function   .

Accepted Answer

A)  0 
B)    
C)    
D)    
E)    
A)  0 
B)    
C)    
D)    
E)

Exam 4: Section 1 : Applications of Differentiation

Locate the absolute extrema of the function on the closed interval .

Sketch the graph of the function and locate the absolute extrema of the function on the interval .

Locate the absolute extrema of the given function on the closed interval .

Locate the absolute extrema of the function on the closed interval .

Find the value of the derivative (if it exists) of the function at the extremum point .

Use a graphing utility to graph the function and locate the absolute extrema of the function on the interval .

Find all critical numbers of of the function , .

Locate the absolute extrema of the function on the closed interval .

Find the value of the derivative (if it exists) of the function at the extremum point .

Locate the absolute extrema of the function on the closed interval .

Use a computer algebra system to graph the function and determine all absolute extrema on the interval .

Locate the absolute extrema of the function on the closed interval .

Locate the absolute extrema of the function on the closed interval . Round your answers to four decimal places.

Use a graphing utility to graph the function and locate the absolute extrema of the function on the interval .

Find all critical numbers of the function .

Find the value of the derivative (if it exists) of at the indicated extremum.

Locate the absolute extrema of the function on the closed interval .

Find all critical numbers of the function , .

Find any critical numbers of the function .

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 2: Applications of Differentiation

Section 3: 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