Home > Calculus > First Derivative Test vs Second Derivative Test for Local Extrema

What is the first derivative test to determine local extrema?

Answer 1

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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Answer 2

Ezekiel Alexander

The first derivative test is a method used to determine local extrema of a function. It states that if a function ( f(x) ) has a critical point at ( x = c ) and ( f'(x) ) changes sign from positive to negative at ( x = c ), then ( f(c) ) is a local maximum. If ( f'(x) ) changes sign from negative to positive at ( x = c ), then ( f(c) ) is a local minimum.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.