Deck 3: Section 4 : Differentiation

Question 1

Find if .

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B)
C)
D)
E)

Answer 1

Question 2

Find the derivative of the function.

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B)
C)
D)
E)

Answer 2

Question 3

Find the derivative of the function.

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B)
C)
D)
E)

Answer 3

Question 4

Differentiate the function .

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B)
C)
D)
E)

Question 5

Find the derivative of the function.

A)
B)
C)
D)
E)

Question 6

Find the derivative of the function.

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B)
C)
D)
E)

Question 7

Find the derivative of the function .

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B)
C)
D)
E)

Question 8

Find the derivative of the function .

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B)
C)
D)
E)

Question 9

Differentiate the function .

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B)
C)
D)
E)

Question 10

Find the derivative of the function . Simplify your answer.

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B)
C)
D)
E)

Question 11

Find the derivative of the algebraic function .

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B)
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D)
E)

Question 12

Find the derivative of the function .

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B)
C)
D)
E)

Question 13

Differentiate the function .

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B)
C)
D)
E)

Question 14

Find the derivative of the function.

A)
B)
C)
D)
E)

Question 15

Find the derivative of the function . Simplify your answer.

A)
B)
C)
D)
E)

Question 16

Find the derivative of the function.

A)
B)
C)
D)
E)

Question 17

Find the derivative of the function .

A)
B)
C)
D)
E)

Question 18

Find if .

A)
B)
C)
D)
E)

Question 19

Find the derivative of the function . Simplify your answer.

A)
B)
C)
D)
E)

Question 20

Find the derivative of the function.

A)
B)
C)
D)
E)

Question 21

Find the second derivative of the function.

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B)
C)
D)
E)

Question 22

Find the second derivative of the function .

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D)
E)

Question 23

Find an equation of the tangent line to the graph of at the point (1,0).

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B)
C)
D)
E)

Question 24

Evaluate the derivative of the function at the point .

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B)
C)
D)
E)

Question 25

Evaluate the derivative of the function at the point .

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B)
C)
D)
E)

Question 26

Find the derivative of the function .

A)
B)
C)
D)
E)

Question 27

Find an equation to the tangent line for the graph of f at the given point. ,

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B)
C)
D)
E)

Question 28

Find if .

A)
B)
C)
D)
E)

Question 29

Find if .

A)
B)
C)
D)
E)

Question 30

Find an equation to the tangent line to the graph of the function at the point . The coefficients below are given to two decimal places.

A)
B)
C)
D)
E)

Question 31

The displacement from equilibrium of an object in harmonic motion on the end of a spring is where y is measured in feet and t is the time in seconds. Determine the position of the object when . Round your answer to two decimal places.

A) 0.12 feet
B) 0.21 feet
C) 17.53 feet
D) 0.46 feet
E) 0.11 feet

Question 32

Evaluate the derivative of the function at the point .

A)
B)
C)
D)
E)

Question 33

Find if .

A)
B)
C)
D)
E)

Question 34

The displacement from equilibrium of an object in harmonic motion on the end of a spring is where y is measured in feet and t is the time in seconds. Determine the velocity of the object when . Round your answer to two decimal places.

A) 8.00 ft/sec
B) 4.68 ft/sec
C) 6.00 ft/sec
D) 1.00 ft/sec
E) 5.00 ft/sec

Question 35

Find the derivative of the function .

A)
B)
C)
D)
E)

Question 36

Find if .

A)
B)
C)
D)
E)

Question 37

Evaluate the derivative of the function at the given point. ,

A)
B)
C)
D)
E)

Question 38

Find the derivative of the function .

A)
B)
C)
D)
E)

Question 39

Find an equation of the tangent line to the graph of at the point .

A)
B)
C)
D)
E)

Question 40

Suppose a 15-centimeter pendulum moves according to the equation where is the angular displacement from the vertical in radians and t is the time in seconds. Determine the rate of change of when t = 7 seconds. Round your answer to four decimal places.

A) 2.5034 radians per second
B) 3.6185 radians per second
C) 0.3129 radians per second
D) 3.1535 radians per second
E) 4.1724 radians per second

Question 41

If the annual rate of inflation averages over the next years, the approximate cost of goods or services during any year in that decade is where is the time in years and is the present cost. The price of an oil change for your car is presently . Find the rate of change of with respect to when . Round your answer to three decimal places.

A) 32.176 dollars per year
B) 1.966 dollars per year
C) 2.293 dollars per year
D) 5.962 dollars per year
E) 32.730 dollars per year

Question 42

A buoy oscillates in simple harmonic motion as waves move past it. The buoy moves a total of 13.5 feet (vertically) between its low point and its high point. It returns to its high point every 10 seconds. Determine the velocity of the buoy as a function of t.

A)
B)
C)
D)
E)

Question 43

A buoy oscillates in simple harmonic motion as waves move past it. The buoy moves a total of 3.5 feet (vertically) between its low point and its high point. It returns to its high point every 14 seconds. Write an equation describing the motion of the buoy if it is at its high point at t = 0.

A)
B)
C)
D)
E)

Question 44

If the annual rate of inflation averages over the next years, the approximate cost of goods or services during any year in that decade is where is the time in years and is the present cost. The price of an oil change for your car is presently . Estimate the price years from now. Round your answer to two decimal places.

A) $26.30
B) $30.67
C) $78.89
D) $25.61
E) $94.31