Question 1

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:   B

Question 2

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:   A

Question 3

Find any critical numbers of the function

Accepted Answer

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

Question 4

The formula for the power output of battery is   is the electromotive force in volts,   is the resistance, and   is the current.Find the current (measured in
Amperes) that corresponds to a maximum value of P in a battery for which   volts and   ohm.Assume that a   ampere fuse bounds the output in the interval   Round your answer
To two decimal places.

Accepted Answer

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

Question 5

A plane begins its takeoff at 2:00 P.M.on a 2200-mile flight.After 12.5 hours, the plane arrives at its destination.Explain why there are at least two times during the flight when the
Speed of the plane is 100 miles per hour.

Accepted Answer

A) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 303 mi/hr.The speed was 100 mi/hr when the plane was accelerating to
303 mi/hr and decelerating from 303 mi/hr. 
B) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 152 mi/hr.The speed was 100 mi/hr when the plane was accelerating to
152 mi/hr and decelerating from 152 mi/hr. 
C) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 88 mi/hr.The speed was 100 mi/hr when the plane was accelerating to 88
Mi/hr and decelerating from 88 mi/hr. 
D) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 117 mi/hr.The speed was 100 mi/hr when the plane was accelerating to
117 mi/hr and decelerating from 117 mi/hr. 
E) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 176 mi/hr.The speed was 100 mi/hr when the plane was accelerating to
176 mi/hr and decelerating from 176 mi/hr. 
A) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 303 mi/hr.The speed was 100 mi/hr when the plane was accelerating to
303 mi/hr and decelerating from 303 mi/hr. 
B) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 152 mi/hr.The speed was 100 mi/hr when the plane was accelerating to
152 mi/hr and decelerating from 152 mi/hr. 
C) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 88 mi/hr.The speed was 100 mi/hr when the plane was accelerating to 88
Mi/hr and decelerating from 88 mi/hr. 
D) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 117 mi/hr.The speed was 100 mi/hr when the plane was accelerating to
117 mi/hr and decelerating from 117 mi/hr. 
E) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 176 mi/hr.The speed was 100 mi/hr when the plane was accelerating to
176 mi/hr and decelerating from 176 mi/hr.

Question 6

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 7

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

Accepted Answer

A) Rolle's Theorem applies;   
B) Rolle's Theorem applies;   
C) Rolle's Theorem applies;   
D) Rolle's Theorem applies;   
E) Rolle's Theorem does not apply 
A) Rolle's Theorem applies;   
B) Rolle's Theorem applies;   
C) Rolle's Theorem applies;   
D) Rolle's Theorem applies;   
E) Rolle's Theorem does not apply

Question 8

The ordering and transportation cost C for components used in a manufacturing process is approximated by   where C is measured in thousands of dollars and x   is the order size in hundreds.According to Rolle's Theorem, the rate of change of the cost must be 0
For some order size in the interval   Find this order size.Round your answer to three decimal
Places.

Accepted Answer

A) 9.657 components 
B) 6.828 components 
C) 8.000 components 
D) 6.000 components 
E) 4.828 components 
A) 9.657 components 
B) 6.828 components 
C) 8.000 components 
D) 6.000 components 
E) 4.828 components

Question 9

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 10

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) c = 8 
B) c = 12, c = 11 
C) c = 11, c = 8 
D) c = 12 
E) Rolle's Theorem does not apply 
A) c = 8 
B) c = 12, c = 11 
C) c = 11, c = 8 
D) c = 12 
E) Rolle's Theorem does not apply

Question 11

Find a function f that has derivative   and with graph passing through the point (5,6).

Accepted Answer

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

Question 12

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 13

Locate the absolute extrema of the function   on the closed interval

Accepted Answer

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

Question 14

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

Accepted Answer

A) Rolle's Theorem applies;   
B) Rolle's Theorem applies;   
C) Rolle's Theorem does apply;   
D) Rolle's Theorem applies;   
E) Rolle's Theorem does not apply 
A) Rolle's Theorem applies;   
B) Rolle's Theorem applies;   
C) Rolle's Theorem does apply;   
D) Rolle's Theorem applies;   
E) Rolle's Theorem does not apply

Question 15

Find all critical numbers of the function

Accepted Answer

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

Question 16

Determine whether the Mean Value Theorem can be applied to the function   on the closed interval [3,9].If the Mean Value Theorem can be applied, find all numbers c in the open interval (3,9) such that

Accepted Answer

A) MVT applies; c = 6 
B) MVT applies; c = 7 
C) MVT applies; c = 4 
D) MVT applies; c = 5 
E) MVT applies; c = 8 
A) MVT applies; c = 6 
B) MVT applies; c = 7 
C) MVT applies; c = 4 
D) MVT applies; c = 5 
E) MVT applies; c = 8

Question 17

Determine whether Rolle's Theorem can be applied to the function   on the closed interval [-1,3].If Rolle's Theorem can be applied, find all values of c in the open interval (-1,3) such that

Accepted Answer

A) Rolle's Theorem applies; c = 1 
B) Rolle's Theorem applies; c = 2 
C) Rolle's Theorem applies; c = 0 
D) Rolle's Theorem applies; c = -1 
E) Rolle's Theorem does not apply 
A) Rolle's Theorem applies; c = 1 
B) Rolle's Theorem applies; c = 2 
C) Rolle's Theorem applies; c = 0 
D) Rolle's Theorem applies; c = -1 
E) Rolle's Theorem does not apply

Question 18

Locate the absolute extrema of the function   on the closed interval

Accepted Answer

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

Question 19

Determine whether the Mean Value Theorem can be applied to the function   on the closed interval [0,16].If the Mean Value Theorem can be applied, find all
Numbers c in the open interval (0,16) such that

Accepted Answer

A)    MVT applies; 
B) MVT applies; 4 
C) MVT applies;   
D) MVT applies; 8 
E) MVT does not apply 
A)    MVT applies; 
B) MVT applies; 4 
C) MVT applies;   
D) MVT applies; 8 
E) MVT does not apply

Question 20

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

Accepted Answer

A) Rolle's Theorem applies; c = 0 
B) Rolle's Theorem applies;   
C) Rolle's Theorem applies;   
D) Rolle's Theorem applies;   
E) Rolle's Theorem does not apply. 
A) Rolle's Theorem applies; c = 0 
B) Rolle's Theorem applies;   
C) Rolle's Theorem applies;   
D) Rolle's Theorem applies;   
E) Rolle's Theorem does not apply.

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

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

Find any critical numbers of the function

A plane begins its takeoff at 2:00 P.M.on a 2200-mile flight.After 12.5 hours, the plane arrives at its destination.Explain why there are at least two times during the flight when the Speed of the plane is 100 miles per hour.

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

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

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

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

Find a function f that has derivative and with graph passing through the point (5,6).

Find all critical numbers of the function

Locate the absolute extrema of the function on the closed interval

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

Find all critical numbers of the function

Determine whether the Mean Value Theorem can be applied to the function on the closed interval [3,9].If the Mean Value Theorem can be applied, find all numbers c in the open interval (3,9) such that

Determine whether Rolle's Theorem can be applied to the function on the closed interval [-1,3].If Rolle's Theorem can be applied, find all values of c in the open interval (-1,3) such that

Locate the absolute extrema of the function on the closed interval

Determine whether the Mean Value Theorem can be applied to the function on the closed interval [0,16].If the Mean Value Theorem can be applied, find all Numbers c in the open interval (0,16) such that

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

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

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

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

Find any critical numbers of the function

A plane begins its takeoff at 2:00 P.M.on a 2200-mile flight.After 12.5 hours, the plane arrives at its destination.Explain why there are at least two times during the flight when the Speed of the plane is 100 miles per hour.

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

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

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

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

Find a function f that has derivative and with graph passing through the point (5,6).

Find all critical numbers of the function

Locate the absolute extrema of the function on the closed interval

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

Find all critical numbers of the function

Determine whether the Mean Value Theorem can be applied to the function on the closed interval [3,9].If the Mean Value Theorem can be applied, find all numbers c in the open interval (3,9) such that

Determine whether Rolle's Theorem can be applied to the function on the closed interval [-1,3].If Rolle's Theorem can be applied, find all values of c in the open interval (-1,3) such that

Locate the absolute extrema of the function on the closed interval

Determine whether the Mean Value Theorem can be applied to the function on the closed interval [0,16].If the Mean Value Theorem can be applied, find all Numbers c in the open interval (0,16) such that

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

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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