Find the critical numbers of the function and describe the behavior offat these numbers.

$\displaystyle f(x) = x^6(x - 2)^5$

I took the derivative using product rule

$\displaystyle f'(x) = 6x^5 (x-2)^5 + x^6 5(x-2)^4$

Then i simplified and set $\displaystyle f'(x) = 0$

$\displaystyle f'(x) = x^5(x-2)^4 [6(x-2) + 5x] = 0$

$\displaystyle f'(x) = x^5(x-2)^4 [6x-12 + 5x] = 0$

$\displaystyle f'(x) = x^5(x-2)^4 (x-12) = 0$

and the three points i got were

$\displaystyle x=0$ $\displaystyle x=2$ and $\displaystyle x=12$

i know 0 is right, but 2 and 12 is wrong.

what am i doing wrong?