# How do use the first derivative test to determine the local extrema #x^2/(3(8-x))#?

It is explained below

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To use the first derivative test to determine the local extrema of the function ( \frac{x^2}{3(8-x)} ):

- Find the first derivative of the function.
- Determine the critical points by setting the derivative equal to zero and solving for ( x ).
- Test the sign of the derivative in the intervals determined by the critical points to identify where the function is increasing or decreasing.
- Determine the nature of the extrema based on the behavior of the derivative.

After finding the critical points and evaluating the derivative's sign around them, you can conclude whether each critical point corresponds to a local maximum, local minimum, or neither.

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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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- What are the absolute extrema of #f(x) =x/(x^2-x+1) in[0,3]#?

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