# Section_ 2.2 Basic Differentiation Rules and Rates of Change

Education

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All Questions

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Multiple Choice

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Q 1

Find the derivative of the function.
A)
B)
C)
D)
E)

Free

Multiple Choice

E

Q 2

Find the derivative of the function.
A)
B)
C)
D)
E)

Free

Multiple Choice

D

Q 3

Use the rules of differentiation to find the derivative of the function .
A)
B)
C)
D)
E)

Free

Multiple Choice

C

Q 4

Find the derivative of the function .
A)
B)
C)
D)
E)

Multiple Choice

Q 5

Use the rules of differentiation to find the derivative of the function .
A)
B)
C)
D)
E)

Multiple Choice

Q 6

Find the derivative of the function .
A)
B)
C)
D)
E)

Multiple Choice

Q 7

Find the derivative of the function .
A)
B)
C)
D)
E)

Multiple Choice

Q 8

Find the slope of the graph of the function at the given value. when
A)
B)
C)
D)
E)

Multiple Choice

Q 9

Find the slope of the graph of the function at the given value. when
A)
B)
C)
D)
E)

Multiple Choice

Q 10

Find the slope of the graph of the function at the given value. when
A)
B)
C)
D)
E)

Multiple Choice

Q 11

Find the slope of the graph of the function at the given value. at
A)
B)
C)
D)
E)

Multiple Choice

Q 12

Find the derivative of the function .
A)
B)
C)
D)
E)

Multiple Choice

Q 13

Find the derivative of the function .
A)
B)
C)
D)
E)

Multiple Choice

Q 14

Find the slope-intercept equation of the line tangent to the graph of when .
A)
B)
C)
D)
E)

Multiple Choice

Q 15

Determine all values of x, (if any),at which the graph of the function has a horizontal tangent.
A)
B)
C) and
D) and
E)The graph has no horizontal tangents.

Multiple Choice

Q 16

Determine all values of x, (if any),at which the graph of the function has a horizontal tangent.
A)
B) and
C) and
D)
E)The graph has no horizontal tangents.

Multiple Choice

Q 17

Determine all values of x, (if any),at which the graph of the function has a horizontal tangent.
A) and
B)
C) and
D)
E)The graph has no horizontal tangents.

Multiple Choice

Q 18

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 1,374 feet tall.Determine the velocity function for the coin.
A)
B)
C)
D)
E)

Multiple Choice

Q 19

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 1364 feet tall.Determine the average velocity of the coin over the time interval .
A)-49
B)15
C)45
D)-45
E)-15

Multiple Choice

Q 20

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)-90
B)-42
C)-27
D)-135
E)-45

Multiple Choice

Q 21

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 1368 feet tall.Find the time required for the coin to reach ground level.Round your answer to the three decimal places.
A)3.082 sec
B)10.677 sec
C)11.152 sec
D)3.362 sec
E)10.523 sec

Multiple Choice

Q 22

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 1380 feet tall.Find velocity of the coin at impact.Round your answer to the three decimal places.
A)-257.371
B)-123.207
C)-111.445
D)-246.414
E)-236.414

Multiple Choice

Q 23

A ball is thrown straight down from the top of a 280-ft building with an initial velocity of -24 ft per second.The position function is .What is the velocity of the ball after 4 seconds?
A)The velocity after 4 seconds is -88 ft per second.
B)The velocity after 4 seconds is -104 ft per second.
C)The velocity after 4 seconds is -152 ft per second.
D)The velocity after 4 seconds is -40 ft per second.
E)The velocity after 4 seconds is -304 ft per second.

Multiple Choice

Q 24

A projectile is shot upwards from the surface of the earth with an initial velocity of 136 meters per second.The position function is .
What is its velocity after 6 seconds?
A)The velocity after 6 seconds is 242.6 meters per second.
B)The velocity after 6 seconds is -165.4 meters per second.
C)The velocity after 6 seconds is 77.2 meters per second.
D)The velocity after 6 seconds is 106.6 meters per second.
E)The velocity after 6 seconds is -194.8 meters per second.

Multiple Choice

Q 25

The volume of a cube with sides of length s is given by .Find the rate of change of volume with respect to s when centimeters.
A)10125 cm

^{2}B)3375 cm^{2}C)225 cm^{2}D)675 cm^{2}E)450 cm^{2} Multiple Choice