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Deck 3: Section 2: Differentiation
Full screen (f)
Question
Determine all values of 
, (if any), at which the graph of the function has a horizontal tangent. 
A)
B)
C)
D)
E) The graph has no horizontal tangents.
, (if any), at which the graph of the function has a horizontal tangent. A)
B)
C)
D)
E) The graph has no horizontal tangents.
Question
Suppose the position function for a free-falling object on a certain planet is given by 
. A silver coin is dropped from the top of a building that is 1372 feet tall. Find the instantaneous velocity of the coin when 
.
A) -96 ft/sec
B) -32 ft/sec
C) -20 ft/sec
D) -144 ft/sec
E) -48 ft/sec
. A silver coin is dropped from the top of a building that is 1372 feet tall. Find the instantaneous velocity of the coin when .A) -96 ft/sec
B) -32 ft/sec
C) -20 ft/sec
D) -144 ft/sec
E) -48 ft/sec
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the slope of the graph of the function at the given value. 
when 
A)
B)
C)
D)
E)
when A)
B)
C)
D)
E)
Question
Suppose the position function for a free-falling object on a certain planet is given by 
. A silver coin is dropped from the top of a building that is 1372 feet tall. Determine the average velocity of the coin over the time interval 
.
A) -113 ft/sec
B) 80 ft/sec
C) 112 ft/sec
D) -112 ft/sec
E) -80 ft/sec
. A silver coin is dropped from the top of a building that is 1372 feet tall. Determine the average velocity of the coin over the time interval .A) -113 ft/sec
B) 80 ft/sec
C) 112 ft/sec
D) -112 ft/sec
E) -80 ft/sec
Question
Determine all values of 
, (if any), at which the graph of the function has a horizontal tangent. 
A)
B)
C)
D)
E) The graph has no horizontal tangents.
, (if any), at which the graph of the function has a horizontal tangent. A)
B)
C)
D)
E) The graph has no horizontal tangents.
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the slope of the graph of the function at the given value. 
when 
A)
B)
C)
D)
E)
when A)
B)
C)
D)
E)
Question
Suppose the position function for a free-falling object on a certain planet is given by 
. A silver coin is dropped from the top of a building that is 1370 feet tall. Determine the velocity function for the coin.
A)
B)
C)
D)
E)
. A silver coin is dropped from the top of a building that is 1370 feet tall. Determine the velocity function for the coin.A)
B)
C)
D)
E)
Question
Find the slope of the graph of the function at the given value. 
when 
A)
B)
C)
D)
E)
when A)
B)
C)
D)
E)
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the rules of differentiation to find the derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the slope of the graph of the function at the given value. 
at 
A)
B)
C)
D)
E)
at A)
B)
C)
D)
E)
Question
Use the rules of differentiation to find the derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the slope-intercept equation of the line tangent to the graph of 
when 
A)
B)
C)
D)
E)
when A)
B)
C)
D)
E)
Question
Determine all values of 
, (if any), at which the graph of the function has a horizontal tangent. 
A)
B)
C)
D)
E) The graph has no horizontal tangents.
, (if any), at which the graph of the function has a horizontal tangent. A)
B)
C)
D)
E) The graph has no horizontal tangents.
Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
A ball is thrown straight down from the top of a 300-ft building with an initial velocity of -12 ft per second. The position function is 
. What is the velocity of the ball after 4 seconds?
A) The velocity after 4 seconds is -76 ft per second.
B) The velocity after 4 seconds is -116 ft per second.
C) The velocity after 4 seconds is -140 ft per second.
D) The velocity after 4 seconds is -52 ft per second.
E) The velocity after 4 seconds is -280 ft per second.
. What is the velocity of the ball after 4 seconds?A) The velocity after 4 seconds is -76 ft per second.
B) The velocity after 4 seconds is -116 ft per second.
C) The velocity after 4 seconds is -140 ft per second.
D) The velocity after 4 seconds is -52 ft per second.
E) The velocity after 4 seconds is -280 ft per second.
Question
The volume of a cube with sides of length s is given by 
. Find the rate of change of volume with respect to 
when 
centimeters.
A) 648 cm2
B) 216 cm2
C) 36 cm2
D) 108 cm2
E) 72 cm2
. Find the rate of change of volume with respect to when centimeters.A) 648 cm2
B) 216 cm2
C) 36 cm2
D) 108 cm2
E) 72 cm2
Question
A projectile is shot upwards from the surface of the earth with an initial velocity of 108 meters per second. The position function is 
. What is its velocity after 7 seconds?
A) The velocity after 7 seconds is 181.7 meters per second.
B) The velocity after 7 seconds is -142.3 meters per second.
C) The velocity after 7 seconds is 39.4 meters per second.
D) The velocity after 7 seconds is 73.7 meters per second.
E) The velocity after 7 seconds is -176.6 meters per second.
. What is its velocity after 7 seconds?A) The velocity after 7 seconds is 181.7 meters per second.
B) The velocity after 7 seconds is -142.3 meters per second.
C) The velocity after 7 seconds is 39.4 meters per second.
D) The velocity after 7 seconds is 73.7 meters per second.
E) The velocity after 7 seconds is -176.6 meters per second.
Question
Suppose the position function for a free-falling object on a certain planet is given by 
. A silver coin is dropped from the top of a building that is 1370 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.
A) -286.705 ft/sec
B) -138.492 ft/sec
C) -111.041 ft/sec
D) -276.984 ft/sec
E) -261.984 ft/sec
. A silver coin is dropped from the top of a building that is 1370 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.A) -286.705 ft/sec
B) -138.492 ft/sec
C) -111.041 ft/sec
D) -276.984 ft/sec
E) -261.984 ft/sec
Question
Suppose the position function for a free-falling object on a certain planet is given by 
. A silver coin is dropped from the top of a building that is 1372 feet tall. Find the time required for the coin to reach ground level. Round your answer to the three decimal places.
A) 2.849 sec
B) 10.273 sec
C) 10.693 sec
D) 3.087 sec
E) 10.091 sec
. A silver coin is dropped from the top of a building that is 1372 feet tall. Find the time required for the coin to reach ground level. Round your answer to the three decimal places.A) 2.849 sec
B) 10.273 sec
C) 10.693 sec
D) 3.087 sec
E) 10.091 sec
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Deck 3: Section 2: Differentiation
1
Determine all values of , (if any), at which the graph of the function has a horizontal tangent.
A)
B)
C)
D)
E) The graph has no horizontal tangents.
, (if any), at which the graph of the function has a horizontal tangent. A)
B)
C)
D)
E) The graph has no horizontal tangents.
2
Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1372 feet tall. Find the instantaneous velocity of the coin when .
A) -96 ft/sec
B) -32 ft/sec
C) -20 ft/sec
D) -144 ft/sec
E) -48 ft/sec
. A silver coin is dropped from the top of a building that is 1372 feet tall. Find the instantaneous velocity of the coin when .A) -96 ft/sec
B) -32 ft/sec
C) -20 ft/sec
D) -144 ft/sec
E) -48 ft/sec
-96 ft/sec
3
Find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
4
Find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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5
Find the slope of the graph of the function at the given value. when
A)
B)
C)
D)
E)
when A)
B)
C)
D)
E)
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Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
6
Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1372 feet tall. Determine the average velocity of the coin over the time interval .
A) -113 ft/sec
B) 80 ft/sec
C) 112 ft/sec
D) -112 ft/sec
E) -80 ft/sec
. A silver coin is dropped from the top of a building that is 1372 feet tall. Determine the average velocity of the coin over the time interval .A) -113 ft/sec
B) 80 ft/sec
C) 112 ft/sec
D) -112 ft/sec
E) -80 ft/sec
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
7
Determine all values of , (if any), at which the graph of the function has a horizontal tangent.
A)
B)
C)
D)
E) The graph has no horizontal tangents.
, (if any), at which the graph of the function has a horizontal tangent. A)
B)
C)
D)
E) The graph has no horizontal tangents.
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
8
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
9
Find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
10
Find the slope of the graph of the function at the given value. when
A)
B)
C)
D)
E)
when A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
11
Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1370 feet tall. Determine the velocity function for the coin.
A)
B)
C)
D)
E)
. A silver coin is dropped from the top of a building that is 1370 feet tall. Determine the velocity function for the coin.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
12
Find the slope of the graph of the function at the given value. when
A)
B)
C)
D)
E)
when A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
13
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
14
Use the rules of differentiation to find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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Unlock for access to all 25 flashcards in this deck.
Unlock Deck
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15
Find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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Unlock for access to all 25 flashcards in this deck.
Unlock Deck
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16
Find the slope of the graph of the function at the given value. at
A)
B)
C)
D)
E)
at A)
B)
C)
D)
E)
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Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
17
Use the rules of differentiation to find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
18
Find the slope-intercept equation of the line tangent to the graph of when
A)
B)
C)
D)
E)
when A)
B)
C)
D)
E)
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Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
19
Determine all values of , (if any), at which the graph of the function has a horizontal tangent.
A)
B)
C)
D)
E) The graph has no horizontal tangents.
, (if any), at which the graph of the function has a horizontal tangent. A)
B)
C)
D)
E) The graph has no horizontal tangents.
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
20
Find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
21
A ball is thrown straight down from the top of a 300-ft building with an initial velocity of -12 ft per second. The position function is . What is the velocity of the ball after 4 seconds?
A) The velocity after 4 seconds is -76 ft per second.
B) The velocity after 4 seconds is -116 ft per second.
C) The velocity after 4 seconds is -140 ft per second.
D) The velocity after 4 seconds is -52 ft per second.
E) The velocity after 4 seconds is -280 ft per second.
. What is the velocity of the ball after 4 seconds?A) The velocity after 4 seconds is -76 ft per second.
B) The velocity after 4 seconds is -116 ft per second.
C) The velocity after 4 seconds is -140 ft per second.
D) The velocity after 4 seconds is -52 ft per second.
E) The velocity after 4 seconds is -280 ft per second.
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
22
The volume of a cube with sides of length s is given by . Find the rate of change of volume with respect to when centimeters.
A) 648 cm2
B) 216 cm2
C) 36 cm2
D) 108 cm2
E) 72 cm2
. Find the rate of change of volume with respect to when centimeters.A) 648 cm2
B) 216 cm2
C) 36 cm2
D) 108 cm2
E) 72 cm2
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
23
A projectile is shot upwards from the surface of the earth with an initial velocity of 108 meters per second. The position function is . What is its velocity after 7 seconds?
A) The velocity after 7 seconds is 181.7 meters per second.
B) The velocity after 7 seconds is -142.3 meters per second.
C) The velocity after 7 seconds is 39.4 meters per second.
D) The velocity after 7 seconds is 73.7 meters per second.
E) The velocity after 7 seconds is -176.6 meters per second.
. What is its velocity after 7 seconds?A) The velocity after 7 seconds is 181.7 meters per second.
B) The velocity after 7 seconds is -142.3 meters per second.
C) The velocity after 7 seconds is 39.4 meters per second.
D) The velocity after 7 seconds is 73.7 meters per second.
E) The velocity after 7 seconds is -176.6 meters per second.
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
24
Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1370 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.
A) -286.705 ft/sec
B) -138.492 ft/sec
C) -111.041 ft/sec
D) -276.984 ft/sec
E) -261.984 ft/sec
. A silver coin is dropped from the top of a building that is 1370 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.A) -286.705 ft/sec
B) -138.492 ft/sec
C) -111.041 ft/sec
D) -276.984 ft/sec
E) -261.984 ft/sec
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
25
Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1372 feet tall. Find the time required for the coin to reach ground level. Round your answer to the three decimal places.
A) 2.849 sec
B) 10.273 sec
C) 10.693 sec
D) 3.087 sec
E) 10.091 sec
. A silver coin is dropped from the top of a building that is 1372 feet tall. Find the time required for the coin to reach ground level. Round your answer to the three decimal places.A) 2.849 sec
B) 10.273 sec
C) 10.693 sec
D) 3.087 sec
E) 10.091 sec
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 25 flashcards in this deck.
