Combined: Calculus Review Applications of Derivatives + Applications of Derivatives + Applic...

Question 1

Find if this equation is continuous/differentiable.

Accepted Answer

Continuous and differentiable

Question 2

Given the graph of f ' (derivative of f), where is f ' negative?

Accepted Answer

(3, 5.5)

Question 3

If f'(x)=(x+2)/(x-3), then the critical number(s) is/are:

Accepted Answer

x = -2 and x = 3

Question 4

Part II (#3)

Accepted Answer

A

Question 5

Part II (#26)

Accepted Answer

D

Question 6

How many values of c satisfy the Mean Value Theorem (MVT) on [a, b]?

Accepted Answer

3

Question 7

Part I (#4)

Accepted Answer

E

Question 8

Find the inflection point for the function f(x)=x4-x .

Accepted Answer

No point of inflection

Question 9

Part I (#25)

Accepted Answer

E

Question 10

Find the answer:

Accepted Answer

continuous but not differentiable

Question 11

Part II (#23)

Accepted Answer

E

Question 12

Find the answer:

Accepted Answer

x=a, x=b, and x=d

Question 13

Find the interval over which the given function is decreasing.

Accepted Answer

(-2, 4)

Question 14

Given the graph of f ' (derivative of f), where does f have a POI?

Accepted Answer

x=5, x=1

Question 15

Given f(x) =x2 , find the value c on the interval [1, 3] for which the MVT applies.

Accepted Answer

x = 2

Question 16

2)

Accepted Answer

B

Question 17

Given the graph of f ' (derivative of f), where is f ' decreasing?

Accepted Answer

(1, 5)

Question 18

All functions satisfy the MVT on [-1, 1] except:

Accepted Answer

x^(3/5)

Question 19

Given the graph of f ' (derivative of f), where is f ' increasing?

Accepted Answer

(0, 1) U (5, 6)

Question 20

Given the graph of f ' (derivative of f), for -6<x<8, where does f has a POI?

Accepted Answer

x=-0.7, x=2, x=5.7

Question 21

Part II (#24)

Accepted Answer

C

Question 22

Given the graph of f ' (derivative of f), for -6<x<8, where does f has a relative max?

Accepted Answer

x=-2

Question 23

Given the graph of f ' (derivative of f), where is f increasing?

Accepted Answer

(0, 3) U (5.5, 6)

Question 24

Given the graph of f ' (derivative of f), for -6<x<8, where is f concave up?

Accepted Answer

(-0.7, 2) U (5.7, 8)

Question 25

What is the value(s) of c that satisfies the MVT on [1, 2] for f(x) = x2 + 5x + 2?

Accepted Answer

3/2

Question 26

Find the interval over which the given function is concave up.

Accepted Answer

(1, ∞)

Question 27

A point of inflection can be found when...

Accepted Answer

f"(x) changes signs

Question 28

Part I (#5)

Accepted Answer

C

Question 29

Part I (#19)

Accepted Answer

E

Question 30

Given the graph of f ' (derivative of f), where is f concave down?

Accepted Answer

(1, 5)

Question 31

Given the graph of f ' (derivative of f), where does f have a relative min?

Accepted Answer

x=5.5

Question 32

At what intervals is this function continuous and differentiable

Accepted Answer

[-3,0) & (0, 3]

Question 33

The Second Derivative Test...

Accepted Answer

Determines if critical points are local extrema on f(x)

Question 34

3)

Accepted Answer

C

Question 35

Part II (#14)

Accepted Answer

B

Question 36

Part I (#3)

Accepted Answer

E

Question 37

Given the graph of f ' (derivative of f), for -6<x<8, where does f has a relative min?

Accepted Answer

x=7

Question 38

5)

Accepted Answer

A

Question 39

Find if this equation is continuous/differentiable at x=2.

Accepted Answer

Continuous and differentiable

Question 40

Find the answer:

Accepted Answer

0

Question 41

Which of the following is NOT a step when completing an optimization problem.

Accepted Answer

Check for change

Question 42

Given the graph of f ' (derivative of f), for -6<x<8, where is f increasing?

Accepted Answer

(-6, -2) U (7, 8)

Question 43

1)

Accepted Answer

B

Question 44

Given the graph of f ' (derivative of f), where is f ' positive?

Accepted Answer

(0, 3) U (5.5, 6)

Question 45

Find if this function is continuous/differentiable.

Accepted Answer

Continuous and differentiable

Question 46

Given the graph of f ' (derivative of f), for -6<x<8, where is f ' positive?

Accepted Answer

(-6, -2) U (7, 8)

Question 47

Part I (#7)

Accepted Answer

D

Question 48

What is the absolute maximum and minimum values of g(x) = 10 - 6x2 on [-2, 5] ?

Accepted Answer

10 and -140

Question 49

If a function is differentiable, then it is continuous.

Accepted Answer

Always TRUE

Question 50

Given the graph of f ' (derivative of f), for -6<x<8, where is f decreasing?

Accepted Answer

(-2, 7)

Question 51

Given the graph of f ' (derivative of f), for -6<x<8, where is f concave down?

Accepted Answer

(-6, -0.7) U (2, 5.7)

Question 52

Part I (#13)

Accepted Answer

C

Question 53

Based on the sign chart, which of the following statements is false?

Accepted Answer

f(x) has three points of inflection

Question 54

Given the graph of f ' (derivative of f), for -6<x<8, where is f ' decreasing?

Accepted Answer

(-6, -0.7) U (2, 5.7)

Question 55

Part I (#21)

Accepted Answer

B

Question 56

Based on the sign chart, which of the following statements is false?

Accepted Answer

f(x) has two critical points

Question 57

Given the graph of f ' (derivative of f), where does f have a relative max?

Accepted Answer

x=3

Question 58

Given the graph of f ' (derivative of f), where is f decreasing?

Accepted Answer

(3, 5.5)

Question 59

7)

Accepted Answer

D

Question 60

Given the graph of f ' (derivative of f), for -6<x<8, where is f ' increasing?

Accepted Answer

(-0.7, 2) U (5.7, 8)

Question 61

Find the answer:

Accepted Answer

I and III

Question 62

The First Derivative Test...

Accepted Answer

Determines if critical points are local extrema on f(x)

Question 63

If f(x) = cos x, then the MVT guarantees somewhere between 0 and π/3, f'(x) =

Accepted Answer

-3/2π

Question 64

Given the graph of f ' (derivative of f), where is f concave up?

Accepted Answer

(0, 1) U (5, 6)

Combined: Calculus Review Applications of Derivatives + Applications of Derivatives + Applic...

Questions 64

Combined: Calculus Review Applications of Derivatives + Applications of Derivatives + Applic...

Questions 64