Deck 3: Applications of Differentiation

Question 1

Find all critical numbers of the function

A)
B)
C)
D)
E)

Answer 1

Question 2

Locate the absolute extrema of the function on the closed interval

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

Answer 2

absolute max: ; absolute min:

Question 3

Find all critical numbers of of the function

A)
B)
C)
D)
E)

Answer 3

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.

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

Question 5

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

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 6

Locate the absolute extrema of the function on the closed interval

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 7

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 8

Find all critical numbers of the function

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

Question 9

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

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

Question 10

Locate the absolute extrema of the function on the closed interval

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

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

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

Question 12

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

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 13

Locate the absolute extrema of the function on the closed interval

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

Locate the absolute extrema of the function on the closed interval

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 15

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

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 16

Locate the absolute extrema of the function on the closed interval

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 17

Find any critical numbers of the function

A)0
B)
C)
D)
E)

Question 18

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 19

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

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 20

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

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

Question 21

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 22

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

Question 23

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 24

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 25

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 26

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 27

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 28

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 29

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 30

Which of the following functions passes through the point and satisfies

A)
B)
C)
D)
E)

Question 31

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 32

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

Question 33

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

A)
B)
C)
D)
E)

Question 34

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