Deck 4: Applications of Derivatives

Question 1

Find the location of the indicated absolute extremum for the function.
Maximum

A) x = 0
B) No maximum
C) x = 2
D) x = -1

Answer 1

C

Question 2

Find the location of the indicated absolute extremum for the function.
Minimum

A) x = 1
B) x = -1
C) x = 2
D) No minimum

Answer 2

D

Question 3

Solve the problem.
Find the graph that matches the given table.

Answer 3

C

Question 4

Find the location of the indicated absolute extremum for the function.
Minimum

A) x = 1
B) x = 2
C) x = -1
D) x = -2

Question 5

Solve the problem.
Find the table that matches the graph below.

Question 6

Find the location of the indicated absolute extremum for the function.
Minimum

A) x = 3
B) x = 5
C) x = -3
D) x = -5

Question 7

Sketch the graph of the function and determine whether it has any absolute extreme values on its domain.

Question 8

Determine from the graph whether the function has any absolute extreme values on the interval [a, b].

A) No absolute extrema.
B) Absolute maximum only.
C) Absolute minimum only.
D) Absolute minimum and absolute maximum.

Question 9

Determine from the graph whether the function has any absolute extreme values on the interval [a, b].

A) Absolute minimum and absolute maximum.
B) Absolute maximum only.
C) No absolute extrema.
D) Absolute minimum only.

Question 10

Solve the problem.
Find the table that matches the given graph.

Question 11

Find the location of the indicated absolute extremum for the function.
Maximum

Question 12

Find the location of the indicated absolute extremum for the function.
Maximum

A) No maximum
B) x = 0
C) x = 3
D) x = 5

Question 13

Find the location of the indicated absolute extremum for the function.
Maximum

A) x = 4
B) x = 1
C) No maximum
D) x = -4

Question 14

Determine from the graph whether the function has any absolute extreme values on the interval [a, b].

A) Absolute minimum and absolute maximum.
B) No absolute extrema.
C) Absolute maximum only.
D) Absolute minimum only.

Question 15

Find the location of the indicated absolute extremum for the function.
Maximum

A) x = 4
B) x = 1
C) No maximum
D) x = -1

Question 16

Solve the problem.
Find the graph that matches the given table.

Question 17

Sketch the graph of the function and determine whether it has any absolute extreme values on its domain.

Question 18

Determine from the graph whether the function has any absolute extreme values on the interval [a, b].

A) Absolute maximum only.
B) Absolute minimum and absolute maximum.
C) No absolute extrema.
D) Absolute minimum only.

Question 19

Find the location of the indicated absolute extremum for the function.
Minimum

A) x = -3
B) x = -4
C) x = 2
D) x = 0

Question 20

Determine from the graph whether the function has any absolute extreme values on the interval [a, b].

A) No absolute extrema.
B) Absolute maximum only.
C) Absolute minimum and absolute maximum.
D) Absolute minimum only.

Question 21

Find the absolute extreme values of the function on the interval.

Question 22

Find the absolute extreme values of the function on the interval.

Question 23

Find the absolute extreme values of the function on the interval.
f(x) = 3x - 4, -2  x 3

A) absolute maximum is 5 at x = -2; absolute minimum is - 2 at x = 3
B) absolute maximum is 13 at x = 3; absolute minimum is - 2 at x = -2
C) absolute maximum is 5 at x = 3; absolute minimum is - 10 at x = -2
D) absolute maximum is 13 at x = -3; absolute minimum is - 10 at x = 2

Question 24

Determine all critical points for the function.

Question 25

Find the absolute extreme values of the function on the interval.

Question 26

Find the absolute extreme values of the function on the interval.

Question 27

Find the absolute extreme values of the function on the interval.

Question 28

Determine all critical points for the function.

Question 29

Find the absolute extreme values of the function on the interval.

Question 30

Determine all critical points for the function.

Question 31

Find the absolute extreme values of the function on the interval.

Question 32

Determine all critical points for the function.

Question 33

Find the absolute extreme values of the function on the interval.

Question 34

Find the absolute extreme values of the function on the interval.

Question 35

Find the absolute extreme values of the function on the interval.
g(x) = -x2 + 8x - 16, 4  x 4

A) absolute maximum is 32 at x = 4; absolute minimum is 0 at 4 and 0 at x = 4
B) absolute maximum is 1 at x = 5; absolute minimum is 0 at 4 and 0 at x = 4
C) absolute maximum is 0 at x = 5; absolute minimum is 0 at 4 and 0 at x = 4
D) absolute maximum is 0 at x = 4; absolute minimum is 0 at 4 and 0 at x = 4

Question 36

Find the absolute extreme values of the function on the interval.

Question 37

Find the absolute extreme values of the function on the interval.

Question 38

Find the absolute extreme values of the function on the interval.

Question 39

Find the absolute extreme values of the function on the interval.

Question 40

Find the absolute extreme values of the function on the interval.

Question 41

Find the extreme values of the function and where they occur.

Question 42

Find the derivative at each critical point and determine the local extreme values.

Question 43

Find the extreme values of the function and where they occur.

Question 44

Find the derivative at each critical point and determine the local extreme values.

Question 45

Find the extreme values of the function and where they occur.

Question 46

Find the extreme values of the function and where they occur.

A) The maximum is 7 at x = 2.
B) The minimum is 7 at x = 0.
C) The minimum is 0 at x = 1.
D) The maximum is 7 at x = -2.

Question 47

Find the extreme values of the function and where they occur.

A) None
B) The maximum is 4 at x = 1.
C) The minimum is 4 at x = -1.
D) The maximum is 4 at x = 2.

Question 48

Find the extreme values of the function and where they occur.

Question 49

Find the derivative at each critical point and determine the local extreme values.

Question 50

Find the extreme values of the function and where they occur.

A) The minimum value is - 1 at x = -1. The maximum value is 1at x = 1.
B) The maximum value is 0 at x = 0.
C) The minimum value is 0 at x = 1. The maximum value is 0 at x = -1.
D) The minimum value is 0 at x = 0.

Question 51

Find the extreme values of the function and where they occur.

Question 52

Determine all critical points for the function.

Question 53

Find the extreme values of the function and where they occur.

A) The minimum value is 0 at x = -5.
B) The maximum value is 0 at x = -5.
C) There are no definable extrema.
D) The minimum value is 0 at x = 5.

Question 54

Find the extreme values of the function and where they occur.

Question 55

Determine all critical points for the function.

Question 56

Determine all critical points for the function.

Question 57

Find the extreme values of the function and where they occur.

Question 58

Find the extreme values of the function and where they occur.

Question 59

Find the derivative at each critical point and determine the local extreme values.

Question 60

Find the extreme values of the function and where they occur.

Question 61

Provide an appropriate response.

Question 62

Provide an appropriate response.
(a) Find the extreme values for P.
(b) Give an interpretation in terms of perimeter of the rectangle for any values found in part (a).

Question 63

Graph the function, then find the extreme values of the function on the interval and indicate where they occur.
b). Find the interior points where f = 0 (you may need to use the numerical equation solver to approximate a
solution). You may wish to plot f as well. List the points as ordered pairs (x, y).
c). Find the interior points where f does not exist. List the points as ordered pairs (x, y).
d). Evaluate the function at the endpoints and list these points as ordered pairs (x, y).
e). Find the function's absolute extreme values on the interval and identify where they occur.

Question 64

Find the derivative at each critical point and determine the local extreme values.

Question 65

Provide an appropriate response.
If the derivative of an even function f(x) is zero at x = c, can anything be said about the value of f at x = -c? Give
reasons for your answer.

Question 66

Graph the function, then find the extreme values of the function on the interval and indicate where they occur.

Question 67

Find the derivative at each critical point and determine the local extreme values.

Question 68

Provide an appropriate response.

Question 69

Graph the function, then find the extreme values of the function on the interval and indicate where they occur.

Question 70

Provide an appropriate response.
maximize profit.

A) 5 hundred thousand
B) 3 hundred thousand
C) 10 hundred thousand
D) 8 hundred thousand

Question 71

Graph the function, then find the extreme values of the function on the interval and indicate where they occur.

Question 72

Provide an appropriate response.

Question 73

Provide an appropriate response.
Imagine there is a function for which f(x) = 0 for all x. Does such a function exist? Is it reasonable to say that all
values of x are critical points for such a function? Is it reasonable to say that all values of x are extreme values
for such a function. Give reasons for your answer.

Question 74

Provide an appropriate response.
If the derivative of an odd function g(x) is zero at x = c, can anything be said about the value of g at x = -c?
Give reasons for you answer.

Question 75

Graph the function, then find the extreme values of the function on the interval and indicate where they occur.
Use the following function and a graphing calculator to answer the questions. b). Find the interior points where f = 0 (you may need to use the numerical equation solver to approximate a
solution). You may wish to plot f as well. List the points as ordered pairs (x, y).
c). Find the interior points where f does not exist. List the points as ordered pairs (x, y).
d). Evaluate the function at the endpoints and list these points as ordered pairs (x, y).
e). Find the function's absolute extreme values on the interval and identify where they occur.

Question 76

Provide an appropriate response.

Question 77

Graph the function, then find the extreme values of the function on the interval and indicate where they occur.
y = x - 1 - x - 6 on the interval -2 < x < 7

Question 78

Provide an appropriate response.

Question 79

Provide an appropriate response.

Question 80

Find the derivative at each critical point and determine the local extreme values.