Deck 4: Extrema on an Interval

Question 1

Answer 1

A

Question 2

Locate the absolute extrema of the function

Answer 2

D

Question 3

Answer 3

C

Question 4

extremum.

Question 5

Question 6

Question 7

Question 8

Determine whether Rolle's Theorem can be applied to the function

Question 9

any critical numbers of the function

Question 10

Question 11

Question 12

Question 13

Question 14

extremum point .

Question 15

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

Question 16

Question 17

all critical numbers of of the function

Question 18

a computer algebra system to graph the function absolute extrema on the interval

Question 19

Locate the absolute extrema of the function

Question 20

Question 21

height of an object t seconds after it is dropped from a height of 550 meters is

Question 22

Identify the open intervals where the function decreasing.

Question 23

company introduces a new product for which the number of units sold S is

Question 24

Identify the open intervals on which the function increasing or decreasing.

Question 25

company introduces a new product for which the number of units sold S is

Question 26

Determine whether the Mean Value Theorem can be applied to the function

Question 27

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 28

height of an object t seconds after it is dropped from a height of 250 meters is

Question 29

Determine whether Rolle's Theorem can be applied to the function

Question 30

Determine whether the Mean Value Theorem can be applied to the function

Question 31

Determine whether the Mean Value Theorem can be applied to the function

Question 32

Determine whether Rolle's Theorem can be applied to the function

Question 33

decreasing.

Question 34

Which of the following functions passes through the point

Question 35

Determine whether Rolle's Theorem can be applied to the function

Question 36

Question 37

Determine whether Rolle's Theorem can be applied to

Question 38

a function f that has derivative the point (5,6).

Question 39

ordering and transportation cost C for components used in a manufacturing

Question 40

intervals on which the function is increasing or decreasing.

Question 41

interval Round numerical values in your answer to three decimal places.

Question 42

the points of inflection and discuss the concavity of the function.

Question 43

Derivative Test.

Question 44

Determine the open intervals on which the graph of is concave downward or concave upward.

Question 45

the points of inflection and discuss the concavity of the function

Question 46

resistance R of a certain type of resistor is where R is measured in ohms and the temperature T is measured in degrees Celsius. Use a computer algebra
System to find

Question 47

all points of inflection on the graph of the function

Question 48

Determine the open intervals on which the graph of the function concave upward or concave downward.

Question 49

the First Derivative Test. Round numerical values in your answer to three decimal places.

Question 50

Then use a graphing utility to confirm your results.

Question 51

ball bearing is placed on an inclined plane and begins to roll. The angle of

Question 52

(a) Find the critical numbers of f (if any); (b) Find the open intervals where the function is increasing or decreasing; and
(c) Apply the First Derivative Test to identify all relative extrema.

Question 53

Determine the open intervals on which the graph of the function

Question 54

downward or concave upward.

Question 55

the open interval(s) on which the function is increasing in the interval Round numerical values in your answer to three decimal places.

Question 56

concave downward or concave upward.

Question 57

the relative minima of the First Derivative Test. Round numerical values in your answer to three decimal places.

Question 58

Question 59

measured in ohms and the temperature T is measured in degrees Celsius. Use a computer algebra system to find the critical number of the function. Round numerical values in your answer to the
Nearest whole number.

Question 60

ball bearing is placed on an inclined plane and begins to roll. The angle of

Question 61

Suppose a manufacturer has determined that the total cost C of operating a factory is

Question 62

all relative extrema of the function . Use the Second Derivative Test where applicable.

Question 63

Match the function with one of the following graphs.

Question 64

all relative extrema of the function . Use the Second Derivative Test where applicable.

Question 65

Question 66

all relative extrema of the function . Use the Second Derivative Test where applicable.

Question 67

all points of inflection on the graph of the function

Question 68

Question 69

the points of inflection and discuss the concavity of the function

Question 70

all points of inflection, if any exist, of the graph of the function

Question 71

Question 72

Locate any relative extrema and inflection points of the function . Use a graphing utility to confirm your results.

Question 73

the points of inflection and discuss the concavity of the function .

Question 74

Suppose the deflection D of a beam of length L is where is the distance from one end of the beam. Find the value of x that yields the maximum deflection.

Question 75

Determine the x-coordinate(s) of any relative extrema and inflection points of the function

Question 76

all points of inflection of the graph of the function the interval . Round your answer to three decimal places wherever applicable.

Question 77

the point of inflection of the graph of the function on the interval

Question 78

all relative extrema of the function . Use the Second Derivative Test where applicable.

Question 79

Determine the x-coordinate(s) of any relative extrema and inflection points of the function

Question 80