# Section 3.2 Rolle’s Theorem and the Mean Value Theorem

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Multiple Choice

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Q 1

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 .
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

Free

Multiple Choice

C

Q 2

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

Free

Multiple Choice

A

Q 3

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 .
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

Free

Multiple Choice

D

Q 4

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 .
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

Multiple Choice

Q 5

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

Multiple Choice

Q 6

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.
A)8.196 components
B)5.598 components
C)6.674 components
D)5.174 components
E)4.098 components

Multiple Choice

Q 7

The height of an object t seconds after it is dropped from a height of 450 meters is .Find the average velocity of the object during the first 3 seconds.Round to two decimal places.
A)14.70 m/sec
B)-14.70 m/sec
C)-9.00 m/sec
D)9.00 m/sec
E)-31.00 m/sec

Multiple Choice

Q 8

The height of an object t seconds after it is dropped from a height of 600 meters is .Find the time during the first 12 seconds of fall at which the instantaneous velocity equals the average velocity.Round to two decimal places,if necessary.
A)72 seconds
B)29.4 seconds
C)10.2 seconds
D)6 seconds
E)2.45 seconds

Multiple Choice

Q 9

Determine whether the Mean Value Theorem can be applied to the function on the closed interval .If the Mean Value Theorem can be applied,find all numbers c in the open interval such that .
A)MVT applies;
B)MVT applies;
C)MVT applies;
D)MVT applies;
E)MVT applies;

Multiple Choice

Q 10

Determine whether the Mean Value Theorem can be applied to the function on the closed interval .If the Mean Value Theorem can be applied,find all numbers c in the open interval such that .
A)MVT applies;
B)MVT applies;4
C)MVT applies;
D)MVT applies;8
E)MVT does not apply

Multiple Choice

Q 11

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.
A)
B)
C)
D)
E)

Multiple Choice

Q 12

Determine whether the Mean Value Theorem can be applied to the function on the closed interval .If the Mean Value Theorem can be applied,find all numbers c in the open interval such that .
A)MVT applies;
B)MVT applies;
C)MVT applies;
D)MVT applies;
E)MVT does not apply

Multiple Choice

Q 13

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?
A)September
B)April
C)November
D)May
E)March

Multiple Choice

Q 14

A plane begins its takeoff at 2:00 P.M.on a 2100-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.
A)By the Mean Value Theorem,there is a time when the speed of the plane must equal the average speed of 290 mi/hr.The speed was 100 mi/hr when the plane was accelerating to 290 mi/hr and decelerating from 290 mi/hr.
B)By the Mean Value Theorem,there is a time when the speed of the plane must equal the average speed of 145 mi/hr.The speed was 100 mi/hr when the plane was accelerating to 145 mi/hr and decelerating from 145 mi/hr.
C)By the Mean Value Theorem,there is a time when the speed of the plane must equal the average speed of 84 mi/hr.The speed was 100 mi/hr when the plane was accelerating to 84 mi/hr and decelerating from 84 mi/hr.
D)By the Mean Value Theorem,there is a time when the speed of the plane must equal the average speed of 112 mi/hr.The speed was 100 mi/hr when the plane was accelerating to 112 mi/hr and decelerating from 112 mi/hr.
E)By the Mean Value Theorem,there is a time when the speed of the plane must equal the average speed of 168 mi/hr.The speed was 100 mi/hr when the plane was accelerating to 168 mi/hr and decelerating from 168 mi/hr.

Multiple Choice

Q 15

Which of the following functions passes through the point and satisfies ?
A)
B)
C)
D)
E)

Multiple Choice

Q 16

Find a function f that has derivative and with graph passing through the point .
A)
B)
C)
D)
E)

Multiple Choice