Deck 4: Derivatives

Question 1

Estimate the slope of the curve at the indicated point.

A) -1
B) 0
C) Undefined
D) 1

Answer 1

B

Question 2

Find an equation for the tangent to the curve at the given point.

Answer 2

C

Question 3

Graph the equation and its tangent.

Answer 3

B

Question 4

Find an equation for the tangent to the curve at the given point.

Question 5

Graph the equation and its tangent.

Question 6

Estimate the slope of the curve at the indicated point.

Question 7

Find an equation for the tangent to the curve at the given point.

Question 8

Find an equation for the tangent to the curve at the given point.

Question 9

Graph the equation and its tangent.

Question 10

Estimate the slope of the curve at the indicated point.

A) Undefined
B) 1
C) -1
D) 0

Question 11

Estimate the slope of the curve at the indicated point.

A) Undefined
B) 1
C) 0
D) -1

Question 12

Estimate the slope of the curve at the indicated point.

A) 1
B) -1
C) 0
D) Undefined

Question 13

Find an equation for the tangent to the curve at the given point.

Question 14

Find an equation for the tangent to the curve at the given point.

Question 15

Graph the equation and its tangent.

Question 16

Estimate the slope of the curve at the indicated point.

Question 17

Estimate the slope of the curve at the indicated point.

A) Undefined
B) 1
C) 0
D) -1

Question 18

Graph the equation and its tangent.

Question 19

Estimate the slope of the curve at the indicated point.

Question 20

Find an equation for the tangent to the curve at the given point.

Question 21

Solve the problem.

Question 22

Solve the problem.

A) 41 mph
B) 5 mph
C) 10 mph
D) 4 mph

Question 23

Solve the problem.
A cubic salt crystal expands by accumulation on all sides. As it expands outward find the rate of change of its volume with respect to the length of an edge when the edge is 0.27 mm.

Question 24

Solve the problem.

Question 25

Provide an appropriate response.

Question 26

Find the slope of the curve at the indicated point.

A) m = 2
B) m = 7
C) m = 4
D) m = 10

Question 27

Solve the problem.

A) 10.6 W/mph
B) 4.8 W/mph
C) 32.8 W/mph
D) 0.5 W/mph

Question 28

Solve the problem.

Question 29

Solve the problem.
Find the points where the graph of the function have horizontal tangents.

Question 30

Solve the problem.

Question 31

Solve the problem.

Question 32

Solve the problem.
Find the points where the graph of the function have horizontal tangents.

Question 33

Find the slope of the curve at the indicated point.

A) m = -16
B) m = -8
C) m = 8
D) m = 16

Question 34

Solve the problem.

Question 35

Solve the problem.

Question 36

Find the slope of the curve at the indicated point.

A) m = -18
B) m = -3
C) m = -12
D) m = 3

Question 37

Solve the problem.

Question 38

Provide an appropriate response.

Question 39

Solve the problem.

Question 40

Find the slope of the curve at the indicated point.

Question 41

Find the indicated derivative.

Question 42

Differentiate the function and find the slope of the tangent line at the given value of the independent variable.

A) -31
B) -1
C) 1
D) 31

Question 43

Find the indicated derivative.

Question 44

Differentiate the function and find the slope of the tangent line at the given value of the independent variable.

Question 45

Differentiate the function and find the slope of the tangent line at the given value of the independent variable.

Question 46

Find an equation of the tangent line at the indicated point on the graph of the function.

Question 47

Calculate the derivative of the function. Then find the value of the derivative as specified.

Question 48

Calculate the derivative of the function. Then find the value of the derivative as specified.

Question 49

Provide an appropriate response.

Question 50

Calculate the derivative of the function. Then find the value of the derivative as specified.

Question 51

Provide an appropriate response.

Question 52

Calculate the derivative of the function. Then find the value of the derivative as specified.

Question 53

Provide an appropriate response.

Question 54

Find the indicated derivative.

Question 55

Calculate the derivative of the function. Then find the value of the derivative as specified.

Question 56

Find the indicated derivative.

Question 57

Calculate the derivative of the function. Then find the value of the derivative as specified.

Question 58

Calculate the derivative of the function. Then find the value of the derivative as specified.

Question 59

Calculate the derivative of the function. Then find the value of the derivative as specified.

Question 60

Calculate the derivative of the function. Then find the value of the derivative as specified.

Question 61

Given the graph of f, find any values of x at which f is not defined.

A) x = -2, 0, 2
B) x = 0
C) x = 2
D) x = -2, 2

Question 62

The graph of a function is given. Choose the answer that represents the graph of its derivative.

Question 63

Question 64

The graph of a function is given. Choose the answer that represents the graph of its derivative.

Question 65

Question 66

Given the graph of f, find any values of x at which f is not defined.

A) x = -3, 3
B) x = -3, 0, 3
C) x = -2, 0, 2
D) x = -2, 2

Question 67

Given the graph of f, find any values of x at which f is not defined.

A) x = 3
B) x = 0, 3
C) x = 0
D) Defined for all values of x

Question 68

Given the graph of f, find any values of x at which f is not defined.

A) x = 2, 5
B) x = 2
C) x = 5
D) Defined for all values of x

Question 69

The graph of a function is given. Choose the answer that represents the graph of its derivative.

Question 70

The graph of a function is given. Choose the answer that represents the graph of its derivative.

Question 71

Question 72

Given the graph of f, find any values of x at which f is not defined.

A) x = 1, 3
B) x = 2
C) x = 1, 2, 3
D) Defined for all values of x

Question 73

Given the graph of f, find any values of x at which f is not defined.

A) x = -2, 2
B) x = 0
C) x = -2, 0, 2
D) Defined for all values of x

Question 74

The graph of a function is given. Choose the answer that represents the graph of its derivative.

Question 75

Question 76

Given the graph of f, find any values of x at which f is not defined.

A) x = 1
B) x = 2
C) x = 0
D) x = 0, 1, 2

Question 77

Given the graph of f, find any values of x at which f is not defined.

A) x = 2
B) x = 0
C) x = 1
D) x = -1

Question 78

Given the graph of f, find any values of x at which f is not defined.

A) x = -1, 1
B) x = 0
C) x = -1, 0, 1
D) Defined for all values of x

Question 79

The graph of a function is given. Choose the answer that represents the graph of its derivative.

Question 80

Find an equation of the tangent line at the indicated point on the graph of the function.