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

##### 1 Answer

Please see below.

#### Explanation:

For

Domain of

# = (x+3)^(2/3)/(3x^(2/3)) + (2x^(1/3))/(3(x+3)^(1/3))#

Get a common denominator and combine to make one quotient.

# = ((x+3)+2x)/(3x^(2/3)(x+3)^(1/3))#

# = (x+1)/(x^(2/3)(x+3)^(1/3))#

and

These are all in the domain of

The graph of

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