# How do you find the critical points for #y = x^(2/3)(x^2-16) #?

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To find the critical points of ( y = x^{2/3}(x^2-16) ), we need to first find the derivative of the function, ( y' ). Then, we set ( y' ) equal to zero and solve for ( x ). Finally, we determine the ( x )-values that make ( y' ) undefined.

First, let's find the derivative of ( y ): [ y' = \frac{d}{dx}(x^{2/3}(x^2-16)) ] [ y' = \frac{d}{dx}(x^{2/3}) \cdot (x^2-16) + x^{2/3} \cdot \frac{d}{dx}(x^2-16) ] [ y' = \frac{2}{3}x^{-1/3}(x^2-16) + x^{2/3} \cdot (2x) ]

Next, set ( y' ) equal to zero and solve for ( x ): [ \frac{2}{3}x^{-1/3}(x^2-16) + 2x^{5/3} = 0 ]

Now, solve for ( x ).

After finding ( x )-values, check for points where the derivative is undefined by checking where the original function ( y ) is undefined or its derivative is undefined.

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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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