# Section 3.3 Increasing and Decreasing Functions and the First Derivative Test

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Multiple Choice

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Q 1

Use the graph of the function given below to estimate the open intervals on which the function is increasing or decreasing.
A)increasing on and
;decreasing on
.
B)increasing on and
;decreasing on
C)increasing on ;decreasing on
and
D)increasing on and
;decreasing on
E)increasing on and
;decreasing on

Free

Multiple Choice

B

Q 2

Identify the open intervals where the function is increasing or decreasing.
A)decreasing on
B)increasing on
C)
D)decreasing on ;increasing on
E)

Free

Multiple Choice

E

Q 3

Identify the open intervals where the function is increasing or decreasing.
A)decreasing: ;increasing:
B)decreasing on
C)increasing: ;decreasing:
D)increasing: ;decreasing:
E)increasing: ;decreasing:

Free

Multiple Choice

D

Q 4

Identify the open intervals on which the function is increasing or decreasing.
A)increasing on ;decreasing on
and
B)increasing on and
;decreasing on
C)increasing on and
;decreasing on
D)increasing on and
;decreasing on
E)increasing on and
decreasing on

Multiple Choice

Q 5

Find the critical number of the function .
A)
B)
C)
D)
E)

Multiple Choice

Q 6

Find the open interval(s)on which is increasing or decreasing.
A)increasing on decreasing on
B)increasing on decreasing on
C)increasing on decreasing on
D)increasing on decreasing on
E)increasing on decreasing on

Multiple Choice

Q 7

Find the relative extremum of by applying the First Derivative Test.
A)relative minimum:
B)relative maximum:
C)relative minimum:
D)relative minimum:
E)relative maximum:

Multiple Choice

Q 8

For the function :
(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.
Then use a graphing utility to confirm your results.
A)(a)
(b)increasing:
;decreasing:
(c)relative max:
;relative min:
B)(a)
(b)decreasing:
;increasing:
(c)relative min:
;relative max:
C)(a)
(b)increasing:
;decreasing:
(c)relative max:
;no relative min.
D)(a)
(b)increasing:
;decreasing:
(c)relative max:
;relative min:
E)(a)
(b)decreasing:
;increasing:
(c)relative min:
;relative max:

Multiple Choice

Q 9

For the function :
(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.
Use a graphing utility to confirm your results.
A)(a)
(b)increasing:
;decreasing:
(c)relative max:
B)(a)
(b)increasing:
;decreasing:
(c)relative max:
C)(a)
(b)decreasing:
;increasing:
(c)relative min:
D)(a)
(b)decreasing:
;increasing:
(c)relative min:
;relative max:
E)(a)
(b)decreasing:
;increasing:
(c)relative min:

Multiple Choice

Q 10

Find the open interval(s)on which the function is increasing in the interval .Round numerical values in your answer to three decimal places.
A)increasing on:
B)increasing on:
C)increasing on:
D)increasing on:
E)increasing on:

Multiple Choice

Q 11

Find the open interval(s)on which the function is decreasing in the interval .Round numerical values in your answer to three decimal places.
A)decreasing on:
B)decreasing on:
C)decreasing on:
D)decreasing on:
E)decreasing on:

Multiple Choice

Q 12

Find the relative maxima of on the interval by applying the First Derivative Test.Round numerical values in your answer to three decimal places.
A)relative maxima:
B)relative maxima:
C)relative maxima:
D)relative maxima:
E)relative maxima:

Multiple Choice

Q 13

Find the relative minima of on the interval by applying the First Derivative Test.Round numerical values in your answer to three decimal places.
A)relative minima:
B)relative minima:
C)relative minima:
D)relative minima:
E)relative minima:

Multiple Choice

Q 14

A ball bearing is placed on an inclined plane and begins to roll.The angle of elevation of the plane is radians.The distance (in meters)the ball bearing rolls in t seconds is .Determine the speed of the ball bearing after t seconds.Round to one decimal place.
A)speed: meters per second
B)speed: meters per second
C)speed: meters per second
D)speed: meters per second
E)speed: meters per second

Multiple Choice

Q 15

A ball bearing is placed on an inclined plane and begins to roll.The angle of elevation of the plane is radians.The distance (in meters)the ball bearing rolls in t seconds is .Determine the value of after one second.Round numerical values in your answer to one decimal place.
A)
B)
C)
D)
E)

Multiple Choice

Q 16

The 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 the critical number of the function.Round numerical values in your answer to the nearest whole number.
A)
B)
C)
D)
E)

Multiple Choice

Q 17

The 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 .
A)
B)
C)
D)
E)

Multiple Choice