# How do you find the critical points for  f(x)=x^3-6x^2+12x-6?

Nov 8, 2015

This is a polynomial , so all derivatives exist . Next, find any x's such that $f ' \left(x\right) = 0$
$f ' \left(x\right) = 3 \left({x}^{2} - 4 x + 4\right) = 0$
$x = 2$ is the only critical point .