Deck 3: Section 3: Differentiation

Question 1

Find the derivative of the algebraic function .

A)
B)
C)
D)
E)

Answer 1

Question 2

Find the derivative of the function .

A)
B)
C)
D)
E)

Answer 2

Question 3

Use the Product Rule to differentiate.

A)
B)
C)
D)
E)

Answer 3

Question 4

The radius of a right circular cylinder is and its height is , where t is time in seconds and the dimensions are in inches. Find the rate of change of the volume of the cylinder, V, with respect to time.

A) cubic inches per second
B) cubic inches per second
C) cubic inches per second
D) cubic inches per second
E) cubic inches per second

Question 5

Use the Product Rule to differentiate .

A)
B)
C)
D)
E)

Question 6

Use the Quotient Rule to differentiate the function .

A)
B)
C)
D)
E)

Question 7

Use the Quotient Rule to differentiate the function .

A)
B)
C)
D)
E)

Question 8

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

A)
B)
C)
D)
E)

Question 9

The length of a rectangle is and its height is , where t is time in seconds and the dimensions are in inches. Find the rate of change of area, A, with respect to time.

A) square inches/second
B) square inches/second
C) square inches/second
D) square inches/second
E) square inches/second

Question 10

Determine all values of x, (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 11

Find the derivative of the function. .

A)
B)
C)
D)
E)

Question 12

Find the derivative of the function . Simplify your answer.

A)
B)
C)
D)
E)

Question 13

Use the Product Rule to differentiate .

A)
B)
C)
D)
E)

Question 14

Use the quotient rule to differentiate the following function and evaluate .

A)
B)
C)
D)
E)

Question 15

Find the derivative of the algebraic function .

A)
B)
C)
D)
E)

Question 16

Use the Quotient Rule to differentiate the function .

A)
B)
C)
D)
E)

Question 17

The ordering and transportation cost C for the components used in manufacturing a product is where C is measured in thousands of dollars and x is the order size in hundreds. Find the rate of change of C with respect to x for x = 24. Round your answer to two decimal places.

A) -6.44 thousand dollars per hundred
B) 8.04 thousand dollars per hundred
C) 3.28 thousand dollars per hundred
D) -4.92 thousand dollars per hundred
E) -7.96 thousand dollars per hundred

Question 18

Find the derivative of the function .

A)
B)
C)
D)
E)

Question 19

A population of 620 bacteria is introduced into a culture and grows in number according to the equation where t is measured in hours. Find the rate at which the population is growing when t = 2. Round your answer to two decimal places.

A) 226.7 bacteria per hour
B) 68.89 bacteria per hour
C) 65.26 bacteria per hour
D) 51.52 bacteria per hour
E) 61.23 bacteria per hour

Question 20

Find the derivative of the trigonometric function .

A)
B)
C)
D)
E)

Question 21

Find the second derivative of the function .

A)
B)
C)
D)
E)

Question 22

Find the second derivative of the function .

A)
B)
C)
D)
E)

Question 23

Given the derivative below find the requested higher-order derivative. .

A)
B)
C)
D)
E)

Question 24

Find the second derivative of the function .

A)
B)
C)
D)
E)

Question 25

Suppose that an automobile's velocity starting from rest is where v is measured in feet per second. Find the acceleration at 9 seconds. Round your answer to one decimal place.

A) 1.9 ft/sec²
B) 0.9 ft/sec²
C) 0.6 ft/sec²
D) 0.2 ft/sec²
E) 8.3 ft/sec²

Question 26

When satellites observe Earth, they can scan only part of Earth's surface. Some satellites have sensors that can measure the angle shown in the figure. Let h represent the satellite's distance from Earth's surface and let r represent Earth's radius. Find the rate at which h is changing with respect to when (Assume r = 4460 miles.) Round your answer to the nearest unit.

A) -2973 mi/radian
B) -5150 mi/radian
C) 5150 mi/radian
D) -8920 mi/radian
E) 2973 mi/radian