Deck 4: Section 2: Applications of Differentiation

Question 1

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.

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

Answer 1

-34.30 m/sec

Question 2

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.

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

Answer 2

4 seconds

Question 3

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

A)
B)
C)
D)
E)

Answer 3

Question 4

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 .

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 5

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

Question 6

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

Question 7

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; 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 8

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.

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 9

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)

Question 10

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 .

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

Question 11

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

Question 12

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

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 13

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

Question 14

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

Question 15

Which of the following functions passes through the point and satisfies ?

A)
B)
C)
D)
E)

Question 16

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

Question 17

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)