# What is the first derivative test to determine local extrema?

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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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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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