Find derivative where f(x) has three products

[cloudboy]

Homework Statement

Trying to find all Max and Min.

F(x) = x^(2/3)(x^2 - 4)

Homework Equations

I know to use the product rule

The Attempt at a Solution

I tried and got this answer:

x^(10/3) + (2(x+2)(x-2)) / 3x^(1/3)

 

[dcassell]

You could also just multiple the x^2/3 through so that you don't have to bother with the product rule.

 

[cloudboy]

Thanks a lot! I got (8(x+1)(x-1)) / (3x^(1/3)) which is the right answer.

 

[ialink]

Using the product rule gives
$\frac{2}{3}$x$^{-1/3}$*(x$^{2}$-4) + 2*x$^{5/3}$

modifying this gives (try it):
x$^{-1/3}$*($\frac{8}{3}$x$^{2}$ - $\frac{8}{3}$)

For min/max equal both factors of this equation to 0 and off course check the domain. Does the expression exist at min/max?