Analyzing f(x), f'(x), and f"(x) (better)
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23 Terms
1
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f’(x) > 0
f(x) is increasing
2
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f’(x) < 0
f(x) is decreasing
3
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f’(x) is changing from - to +
f(x) has a local minimum
4
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f’(x) is changing from + to -
f(x) has a local maximum
5
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f’(x) is increasing
f(x) is concave up
6
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f’(x) is decreasing
f(x) is concave down
7
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f’(x) has an extreme value
f(x) has a point of inflection
8
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f’(x) has an x-int
f(x) has a rel min/max
9
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(x,0)
f”(x) has a POI
10
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f”(x) > 0
f(x) is concave up
11
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f”(x) < 0
f(x) is concave down
12
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when f’(x) stops at zero and doesn’t go through the x-axis
f(x) does not have a rel max/min
13
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when f(x) changes from concave up to concave down (or vice versa)
when do POI occur on f(x)
14
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when f’(x) changes signs
given f’(x), f(x) has a max/min
15
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f”(x) > 0
given f’(x), f’(x) is increasing
16
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f”(x) < 0
given f’(x), f’(x) is decreasing
17
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f”(x) has an x-int
given f”(x), f(x) has a POI
18
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f”(x) > 0
given f”(x), f’(x) is increasing
19
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f”(x) < 0
given f”(x), f’(x) is decreasing
20
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f(x) is increasing
f’(x) and f”(x) have all positive values
21
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f(x) is decreasing
f’(x) and f”(x) have all negative values
22
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closed intervals
when answering a question along the lines of “on what intervals is f increasing/decreasing?” what kinds of intervals are you using?
23
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open intervals
when answering a question along the lines of “on what intervals is f concave up/down?” what kind of interval are you using?
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Flashcards (40)