By the Remainder's Theorem, in which we learned in Algebra, we know that the possible zeroes for a polynoimal is: .
Therefore, the possible list of zeroes here is:
Then just try and find which one would be your zero. I plugged in and it gave me zero, so that is one of your critical points. Check to see if there are any more critical points.
By the way, the factorization of f' here is
That should help.