Critical Numbers

[Calc12]

Hello,

I am trying to find the critical numbers for

f'(x) = 36x^3 - 72x^2 - 72

I got it to:
36(x^3 - 2x^2 - 2)

However, I am confused to as if I am supposed to factor it more? If so how would I factor it further?
Or how would I solve for
36(x^3 - 2x^2 - 2) = 0

Thanks very much in advance.

 

[lookagain]

Calc12,

\(\displaystyle \ 1) \ \ Work \ out \ f'(x). \ \ You'll \ get \ a \ quadratic. \ \ There \ will \ be \ no \ nonzero \ constant\)

\(\displaystyle \ after \ that \ step. \ (In \ this \ case \ it \ will \ be \ equal \ to \ 0).\)


\(\displaystyle \ 2) \ \ Set \ this \ derivative \ equal \ to \ 0 \ and \ solve \ for \ the \ critical \ numbers.\)

\(\displaystyle a) \ \ Factor \ out \ the \ greatest \ common \ factor.\)

\(\displaystyle b) \ \ Set \ each \ factor \ (monomial \ or \ binomial) \ equal \ to \ 0 \ and \ solve \ for \ the \ real \ \ x-values\)

\(\displaystyle (critical \ numbers.)\)

 

[Calc12]

Thanks so much for your time.

However, it seems like I added wrong in the first derivate test :| drove me crazy and I figured it out
I appreciate your help!!