# How do you find the critical points if #f'(x)=2-x/(x+2)^3#?

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To find the critical points of ( f'(x) = \frac{2 - x}{(x + 2)^3} ), we first set the derivative equal to zero and solve for ( x ). Then, we check for points where the derivative is undefined.

- Set ( f'(x) = 0 ):

[ \frac{2 - x}{(x + 2)^3} = 0 ]

- Solve for ( x ):

[ 2 - x = 0 ] [ x = 2 ]

- Check for points where the derivative is undefined. The derivative is undefined when the denominator is equal to zero:

[ (x + 2)^3 = 0 ] [ x = -2 ]

Thus, the critical points of ( f(x) ) occur at ( x = 2 ) and ( x = -2 ).

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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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