Finding Critical Points of a Polynomial

Given the polynomial function $$ f(x) = 3x^4 - 12x^3 + 9x^2 $$, determine the value of $$ x $$ for which the first derivative, $$ f'(x) $$, equals zero.

Start by finding the first derivative of the function using the power rule. Then, solve for $$ x $$ when $$ f'(x) = 0 $$.