Solution
= Solution
The <derivative> factors as
$$
g'(x)=4x^3-24x^2+36x=4x(x-3)^2.
$$
The <polynomial> is differentiable everywhere, so its <critical points> occur precisely where this <derivative> vanishes. Hence
$$
\boxed{x=0\quad\text{and}\quad x=3.}
$$
Their values are $g(0)=5$ and $g(3)=32$.