# Math Help - [SOLVED] Critical Numbers

1. ## [SOLVED] Critical Numbers

I need to find the critical numbers of the function f(x)=x(2-x)^2/5

I found the derivative to be f'(x)= -(2/5)x (2-x)^(-3/5) + (2-x)^(2/5)

But now I'm at a loss at how to factor the equation to find the values for x. Could someone give me a push in the right direction? Any help would be appreciated. Thanks!

2. Originally Posted by yzobel
I need to find the critical numbers of the function f(x)=x(2-x)^2/5

I found the derivative to be f'(x)= -(2/5)x (2-x)^(-3/5) + (2-x)^(2/5)

But now I'm at a loss at how to factor the equation to find the values for x. Could someone give me a push in the right direction? Any help would be appreciated. Thanks!
Your derivative factorises as $(2 - x)^{-3/5} \left( - \frac{2}{5} x + (2 - x)\right)$ ....