Question 1

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

Accepted Answer

A)  13 
B)  0 
C)  15 
D)  -15 
E) does not exist 
A)  13 
B)  0 
C)  15 
D)  -15 
E) does not exist

Question 2

A company introduces a new product for which the number of units sold S is   where t is the time in months since the product was introduced.During what month does   equal the average value of   during the first year?

Accepted Answer

A) October 
B) July 
C) December 
D) April 
E) March 
A) October 
B) July 
C) December 
D) April 
E) March

Question 3

Determine whether Rolle's Theorem can be applied to   on the closed interval   If Rolle's Theorem can be applied, find all values of c in the open interval   such that

Accepted Answer

A) Rolle's Theorem applies; c = 6, c = 5 
B) Rolle's Theorem applies; c = 4, c = 6 
C) Rolle's Theorem applies; c = 5 
D) Rolle's Theorem applies; c = 4 
E) Rolle's Theorem does not apply 
A) Rolle's Theorem applies; c = 6, c = 5 
B) Rolle's Theorem applies; c = 4, c = 6 
C) Rolle's Theorem applies; c = 5 
D) Rolle's Theorem applies; c = 4 
E) Rolle's Theorem does not apply

Question 4

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 5

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 6

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 7

Find all critical numbers of of the function

Accepted Answer

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

Question 8

The height of an object t seconds after it is dropped from a height of 550 meters is   Find the average velocity of the object during the first 7 seconds.

Accepted Answer

A) 34.30 m/sec 
B) -34.30 m/sec 
C) -49.00 m/sec 
D) 49 m/sec 
E) -16.00 m/sec 
A) 34.30 m/sec 
B) -34.30 m/sec 
C) -49.00 m/sec 
D) 49 m/sec 
E) -16.00 m/sec

Question 9

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:

Question 10

The height of an object t seconds after it is dropped from a height of 250 meters is   Find the time during the first 8 seconds of fall at which the
Instantaneous velocity equals the average velocity.

Accepted Answer

A) 32 seconds 
B) 19.6 seconds 
C) 6.38 seconds 
D) 4 seconds 
E) 2.45 seconds 
A) 32 seconds 
B) 19.6 seconds 
C) 6.38 seconds 
D) 4 seconds 
E) 2.45 seconds

Question 11

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 12

Which of the following functions passes through the point   and satisfies

Accepted Answer

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

Question 13

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   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   = 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   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   = 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 14

A company introduces a new product for which the number of units sold S is   where t is the time in months since the product was introduced.Find
The average value of   during the first year.

Accepted Answer

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

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

A company introduces a new product for which the number of units sold S is where t is the time in months since the product was introduced.During what month does equal the average value of during the first year?

Determine whether Rolle's Theorem can be applied to on the closed interval If Rolle's Theorem can be applied, find all values of c in the open interval such that

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

Find all critical numbers of of the function

The height of an object t seconds after it is dropped from a height of 550 meters is Find the average velocity of the object during the first 7 seconds.

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

The height of an object t seconds after it is dropped from a height of 250 meters is Find the time during the first 8 seconds of fall at which the Instantaneous velocity equals the average velocity.

Locate the absolute extrema of the function on the closed interval

Which of the following functions passes through the point and satisfies

Locate the absolute extrema of the function on the closed interval

A company introduces a new product for which the number of units sold S is where t is the time in months since the product was introduced.Find The average value of during the first year.

Limits and Their Properties

Differentiation

Integration

Logarithmic, Exponential, and Other Transcendental Functions

Differential Equations

Applications of Integration

Integration Techniques, Lhôpitals Rule, and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Analysis

Additional Topics in Differential Equations

Preparation for Calculus

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Exam 3: Applications of Differentiation

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

A company introduces a new product for which the number of units sold S is where t is the time in months since the product was introduced.During what month does equal the average value of during the first year?

Determine whether Rolle's Theorem can be applied to on the closed interval If Rolle's Theorem can be applied, find all values of c in the open interval such that

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

Find all critical numbers of of the function

The height of an object t seconds after it is dropped from a height of 550 meters is Find the average velocity of the object during the first 7 seconds.

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

The height of an object t seconds after it is dropped from a height of 250 meters is Find the time during the first 8 seconds of fall at which the Instantaneous velocity equals the average velocity.

Locate the absolute extrema of the function on the closed interval

Which of the following functions passes through the point and satisfies

Locate the absolute extrema of the function on the closed interval

A company introduces a new product for which the number of units sold S is where t is the time in months since the product was introduced.Find The average value of during the first year.

Limits and Their Properties

Differentiation

Integration

Logarithmic, Exponential, and Other Transcendental Functions

Differential Equations

Applications of Integration

Integration Techniques, Lhôpitals Rule, and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Analysis

Additional Topics in Differential Equations

Preparation for Calculus

Filters