# How do you find the critical numbers for #f(x) = x^(1/3)*(x+3)^(2/3)# to determine the maximum and minimum?

Please see below.

Get a common denominator and combine to make one quotient.

graph{ x^(1/3)(x+3)^(2/3) [-7.024, 7.02, -3.51, 3.514]}

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To find the critical numbers for ( f(x) = x^{1/3} \cdot (x+3)^{2/3} ) and determine the maximum and minimum, follow these steps:

- Compute the derivative of ( f(x) ) using the product rule and simplify the expression.
- Set the derivative equal to zero and solve for ( x ) to find the critical numbers.
- Evaluate ( f(x) ) at each critical number and at the endpoints of the domain to determine the maximum and minimum values of the function.

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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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