Deck 3: The Derivative and the Tangent Line Problem

Question 1

Answer 1

B

Question 2

Answer 2

C

Question 3

Answer 3

D

Question 4

Question 5

the derivative of the following function using the limiting process.

Question 6

Question 7

the slope

Question 8

Question 9

the alternative form of the derivative to find the derivative of the function

Question 10

Question 11

Question 12

the derivative of the following function using the limiting process.

Question 13

Question 14

Question 15

the alternative form of the derivative to find the derivative of the function

Question 16

the derivative of the following function using the limiting process.

Question 17

Question 18

Identify the graph which has the following characteristics.

Question 19

the derivative of the following function using the limiting process.

Question 20

Question 21

Question 22

the slope of the graph of the function at the given value.

Question 23

the slope of the graph of the function at the given value.

Question 24

Question 25

Question 26

the slope of the graph of the function at the given value.

Question 27

the derivative of the function.

Question 28

the slope of the graph of the function at the given value.

Question 29

Suppose the position function for a free-falling object on a certain planet is given by

Question 30

Question 31

Question 32

Question 33

Suppose the position function for a free-falling object on a certain planet is given by

Question 34

Determine all values of , (if any), at which the graph of the function has a

Question 35

Question 36

Question 37

the derivative of the function.

Question 38

Determine all values of , (if any), at which the graph of the function has a

Question 39

Question 40

Question 41

the Product Rule to differentiate.

Question 42

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Question 44

the derivative of the function.

Question 45

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Question 47

Suppose the position function for a free-falling object on a certain planet is given by

Question 48

Question 49

Suppose the position function for a free-falling object on a certain planet is given by

Question 50

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Question 52

projectile is shot upwards from the surface of the earth with an initial velocity of

Question 53

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Question 56

ball is thrown straight down from the top of a 300-ft building with an initial

Question 57

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Question 59

Suppose the position function for a free-falling object on a certain planet is given by

Question 60

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Question 62

measured in feet per second. Find the acceleration at 9 seconds. Round your answer to one decimal place.

Question 63

the dimensions are in inches. Find the rate of change of area, A, with respect to time.

Question 64

Determine all values of x, (if any), at which the graph of the function has a horizontal tangent.

Question 65

Question 66

the derivative of the function.

Question 67

Question 68

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.

Question 69

the derivative of the function.

Question 70

Question 71

the derivative of the function.

Question 72

Question 73

ordering and transportation cost C for the components used in manufacturing a

Question 74

the derivative of the function.

Question 75

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

Question 76

population of 620 bacteria is introduced into a culture and grows in number

Question 77

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

Question 78

satellites observe Earth, they can scan only part of Earth's surface. Some

Question 79

the derivative of the function.

Question 80