Behaviors of F(x), F'(x), & F''(x)

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13 Terms

1
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When f(x) is increasing, what do we know about f’(x)?

It is positive

2
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When f(x) is decreasing, what do we know about f’(x)?

It is negative

3
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When f(x) has a horizontal tangent, what do we know about f’(x)?

f’(x) = 0

4
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When f(x) = 0 what do we know about f’(x)?

It has a horizontal tangent

5
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When f(x) has a local max, what do we know about f’(x)?

f’(x) = 0 or is undefined

6
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When f(x) has a local min, what do we know about f’(x)?

f’(x) = 0 or is undefined

7
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When f’(x) has a local max, what do we know about f(x)?

f(x) = 0 or is undefined

8
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When f’(x) has a local min, what do we know about f(x)?

f(x) = 0 or is undefined

9
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when f(x) has a local max, how does f’(x) respond?

f’(x) > 0 to the left & f’(x) < 0 tot he right

10
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when f(x) is concave up what is the behavior of f’(x)?

f’(x) is increasing

11
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when f(x) is concave down what is the behavior of f’(x)?

f’(x) is decreasing

12
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when f(x) is concave up and f’(x) is increasing, what is the behavior of f’’(x) ?

f’’(x) is positive

13
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when f(x) is concave down and f’(x) is decreasing, what is the behavior of f’’(x) ?

f’’(x) is negative