What is the first derivative test for local extreme values?

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

The first derivative test for local extreme values states that if a function ( f(x) ) is continuous on an interval ( (a, b) ) and has a critical point at ( c ) in that interval:

  1. If ( f'(x) ) changes sign from positive to negative at ( c ), then ( f(c) ) is a local maximum.
  2. If ( f'(x) ) changes sign from negative to positive at ( 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.

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.

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.

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.

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