What derivatives tell us about a function
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Last updated 4:44 AM on 12/9/22
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15 Terms
1
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If the derivative is positive
the function is increasing
2
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the derivative is negative
the function is decreasing.
3
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When the derivative equals zero
the original function has a maximum or minimum.
4
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When the derivative changes from positive to negative
the function has a maximum at that point.
5
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When the derivative changes from negative to positive
the function has a minimum at that point.
6
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If the derivative does not change sign at some point c
then f has no minimum or maximum at that point
7
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If the second derivative is positive
the function is concave up.
8
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If the second derivative is negative
the function is concave down.
9
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When the second derivative equals zero
the original function has an inflection point.
10
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When the second derivative changes from positive to negative
the original function changes from concave up to concave down.
11
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When the second derivative changes from negative to positive
the original function changes from concave down to concave up.
12
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If the derivative is increasing over an interval
then the function is concave up over that interval
13
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If the derivative is decreasing over an interval
then the function is concave down over that interval
14
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If the first derivative equals zero, and the second derivative is greater than zero
the original function has a local minimum at that point.
15
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If the first derivative equals zero, and the second derivative is less than zero
the original function has a local maximum at that point.