f, f', f''

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Calculus, f', f'', first derivative and second derivatives on graphs

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Questions 17

Answers

1
Given f'(x), where does f(x) have a local minimum value
x = 0
x = 4
x = 2
x = 0 or x = 4
2
Use the graph of f'(x) to find where f(x) has critical values.
x=2
x = 0, x = 2, or x = 4
x=0
x= 0 or x = 4
3
Where does f(x) have a maximum value?
x = -2
x = -2 or x = 4
x = 0
x ≈ -1.1
4
Where does f(x) appear to be concave up?
(2, ∞)
(-∞, 0) U (4, ∞)
All real numbers
5
This is the graph of f''(x). Where does f(x) have an inflection point?
x = {-5, 0, 5}
x = {-3, 3}
x = 0
Cannot be determined
6
Where does f(x) have an inflection point?
x = 0
x = 4
x = 2
No inflection points
7
At x=-2, order f, f', and f'' from least to greatest
f ''(-2) < f '(-2) < f(-2)
f(-2) < f '(-2)<f ''(-2)
f(-2)<f ''(-2)<f '(-2)
f ''(-2) < f(-2) < f '(-2)
8
Where does f(x) have a local maximum?
x = -3
x = -5 or x = 2
x = -3 or x = 0
x ≈ -4.4 or x = 0
9
Given the graph of f'(x), on what intervals is f(x) increasing?
[4, ∞)
(-∞, 0] U [4, ∞)
[0, 4]
[2, ∞)
10
Where does f(x) have critical values?
x= -2, 0, or 4
No Critical values
x ≈ -1.1 or 2.4
x = 0
11
Where does f(x) have inflection points?
x ≈ {-1.1, 2.4}
x = {-2, 0, 4}
x= 1
12
Note that this is the graph of f(x). Where does f(x) have critical values?
x ≈ -1.1
x ≈ -1.1 or x ≈ 2.4
x = -2, x = 0, or x = 4
x = -2
13
Where does f(x) have an inflection point?
x = -3 or x = 0
x ≈ -4.4 or x = 0
x = {-4.4, -2, 0, 1.3)
x = -5 or x = 2
14
Where are the slopes of f(x) positive?
(-5, -3) U (2, ∞)
(2, ∞)
(1.4, ∞)
(-∞, -4.4) U (-2, 0) U (1.4, ∞)
15
Where is f(x) decreasing?
[-2, 0]
[-2, 0] U [4, ∞)
(-1.1, 2.4)
(-∞, -2] U [0, 4]
16
Where is f'(x) positive?
(-∞, -1.1) U (2.4, ∞)
(-∞, -1.1)
(-2,0) U (4, 0)
(-2, 0)
17
Where is f(x) concave down?
(-∞, 1)
(-∞, -1.1) U (2.4, ∞)
(-2, 0)
(-1.1, 2.4)

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