(Calc Ch 3) Interpreting f, f', f'', from graphs

Question 1

Where is f'(x) positive?

Accepted Answer

(-∞, -1.1) U (2.4, ∞)

Question 2

Where does f(x) have a local maximum?

Accepted Answer

x = -3

Question 3

Use the graph of f'(x) to find where f(x) has critical values.

Accepted Answer

x= 0 or x = 4

Question 4

Where does f(x) have an inflection point?

Accepted Answer

x = 2

Question 5

Where does f(x) have an inflection point?

Accepted Answer

x = {-4.4, -2, 0, 1.3)

Question 6

Where is f(x) decreasing?

Accepted Answer

(-∞, -2] U [0, 4]

Question 7

Where does f(x) have critical values?

Accepted Answer

x= -2, 0, or 4

Question 8

Given f'(x), where does f(x) have a local minimum value

Accepted Answer

x = 4

Question 9

Note that this is the graph of f(x). Where does f(x) have critical values?

Accepted Answer

x ≈ -1.1 or x ≈ 2.4

Question 10

At x=-2, order f, f', and f'' from least to greatest

Accepted Answer

f ''(-2) < f(-2) < f '(-2)

Question 11

Where does f(x) have a maximum value?

Accepted Answer

x = 0

Question 12

Where does f(x) appear to be concave up?

Accepted Answer

(2, ∞)

Question 13

Where does f(x) have inflection points?

Accepted Answer

x ≈ {-1.1, 2.4}

Question 14

Where are the slopes of f(x) positive?

Accepted Answer

(-5, -3) U (2, ∞)

Question 15

When does the particle reach it's maximum height?

Accepted Answer

t = 5

Question 16

Given the graph of f'(x), on what intervals is f(x) increasing?

Accepted Answer

(-∞, 0] U [4, ∞)

Question 17

This is the graph of f''(x). Where does f(x) have an inflection point?

Accepted Answer

x = {-5, 0, 5}

Question 18

Where is f(x) concave down?

Accepted Answer

(-∞, 1)

Questions 18