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Deck 4: Section 3: Applications of Differentiation
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Question
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 
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 
Question
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)
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)
Question
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:
by applying the First Derivative Test.A) relative minimum:
B) relative maximum:
C) relative minimum:
D) relative minimum:
E) relative maximum:
Question
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:
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:
Question
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)
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)
Question
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: 
is increasing or decreasing.A) decreasing:
; increasing: B) decreasing on
C) increasing:
; decreasing: D) increasing:
; decreasing: E) increasing:
; decreasing: Question
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.
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
radians. The distance (in meters) the ball bearing rolls in t seconds is . Determine the speed of the ball bearing after t seconds.A) speed:
meters per secondB) speed:
meters per secondC) speed:
meters per secondD) speed:
meters per secondE) speed:
meters per second Question
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:
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:
Question
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:
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:
Question
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)
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)
Question
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:
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:
Question
Identify the open intervals on which the function 
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 
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 Question
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:
: (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:
Question
Identify the open intervals where the function 
is increasing or decreasing.
A) decreasing on
B) increasing on
C)
D) decreasing on
; increasing on 
E)
is increasing or decreasing.A) decreasing on
B) increasing on
C)
D) decreasing on
; increasing on E)
Question
Use the graph of the function 
given below to estimate the open intervals on which the function 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 
given below to estimate the open intervals on which the function 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 Question
Find the critical number of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
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) x = 0 ,
(b) increasing:
; decreasing: 
(c) relative max:
; relative min: 
B) (a) x = 0 ,
(b) decreasing:
; increasing: 
(c) relative min:
; relative max: 
C) (a) x = 0 ,
(b) increasing:
; decreasing: 
(c) relative max:
; no relative min.
D) (a) x = 0 ,
(b) increasing:
; decreasing: 
(c) relative max:
; relative min: 
E) (a) x = 0 ,
(b) decreasing:
; increasing: 
(c) relative min:
; relative max: 
: (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) x = 0 ,
(b) increasing:
; decreasing: (c) relative max:
; relative min: B) (a) x = 0 ,
(b) decreasing:
; increasing: (c) relative min:
; relative max: C) (a) x = 0 ,
(b) increasing:
; decreasing: (c) relative max:
; no relative min.D) (a) x = 0 ,
(b) increasing:
; decreasing: (c) relative max:
; relative min: E) (a) x = 0 ,
(b) decreasing:
; increasing: (c) relative min:
; relative max: 
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Deck 4: Section 3: Applications of Differentiation
1
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
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 increasing on decreasing on
decreasing on 2
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)
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)
3
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:
by applying the First Derivative Test.A) relative minimum:
B) relative maximum:
C) relative minimum:
D) relative minimum:
E) relative maximum:
relative maximum:
4
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:
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:
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5
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)
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)
Unlock Deck
Unlock for access to all 17 flashcards in this deck.
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k this deck
6
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:
is increasing or decreasing.A) decreasing:
; increasing: B) decreasing on
C) increasing:
; decreasing: D) increasing:
; decreasing: E) increasing:
; decreasing: Unlock Deck
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7
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.
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
radians. The distance (in meters) the ball bearing rolls in t seconds is . Determine the speed of the ball bearing after t seconds.A) speed:
meters per secondB) speed:
meters per secondC) speed:
meters per secondD) speed:
meters per secondE) speed:
meters per second Unlock Deck
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k this deck
8
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:
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:
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Unlock for access to all 17 flashcards in this deck.
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k this deck
9
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:
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:
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k this deck
10
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)
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)
Unlock Deck
Unlock for access to all 17 flashcards in this deck.
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k this deck
11
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:
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:
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k this deck
12
Identify the open intervals on which the function 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
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 Unlock Deck
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k this deck
13
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:
: (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:
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14
Identify the open intervals where the function is increasing or decreasing.
A) decreasing on
B) increasing on
C)
D) decreasing on ; increasing on
E)
is increasing or decreasing.A) decreasing on
B) increasing on
C)
D) decreasing on
; increasing on E)
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k this deck
15
Use the graph of the function given below to estimate the open intervals on which the function 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
given below to estimate the open intervals on which the function 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 Unlock Deck
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16
Find the critical number of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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17
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) x = 0 ,
(b) increasing: ; decreasing:
(c) relative max: ; relative min:
B) (a) x = 0 ,
(b) decreasing: ; increasing:
(c) relative min: ; relative max:
C) (a) x = 0 ,
(b) increasing: ; decreasing:
(c) relative max: ; no relative min.
D) (a) x = 0 ,
(b) increasing: ; decreasing:
(c) relative max: ; relative min:
E) (a) x = 0 ,
(b) decreasing: ; increasing:
(c) relative min: ; relative max:
: (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) x = 0 ,
(b) increasing:
; decreasing: (c) relative max:
; relative min: B) (a) x = 0 ,
(b) decreasing:
; increasing: (c) relative min:
; relative max: C) (a) x = 0 ,
(b) increasing:
; decreasing: (c) relative max:
; no relative min.D) (a) x = 0 ,
(b) increasing:
; decreasing: (c) relative max:
; relative min: E) (a) x = 0 ,
(b) decreasing:
; increasing: (c) relative min:
; relative max: Unlock Deck
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Unlock for access to all 17 flashcards in this deck.
