What is the first derivative test for local extreme values?

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What is the first derivative test for local extreme values?

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Answer 1 · 2014-09-22T23:06:27

First Derivative Test for Local Extrema
Let #x=c# be a critical value of #f(x)#.
If #f'(x)# changes its sign from + to - around #x=c#, then #f(c)# is a local maximum.
If #f'(x)# changes its sign from - to + around #x=c#, then #f(c)# is a local minimum.
If #f'(x)# does not change its sign around #x=c#, then #f(c)# is neither a local maximum nor a local minimum.

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What is the first derivative test for local extreme values?

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