Maximum Value of a Polynomial Function

Let $$ f(x) = x^3 - 6x^2 + 9x $$ be a polynomial function defined for all real numbers.

To analyze the behavior of the function, we first need to find the critical points by computing the derivative $$ f'(x) $$ and then setting it to zero. Determine the critical points, and then evaluate the function at these critical points to find the maximum value of $$ f(x) $$ in this interval.