Finding Local Maximum of a Cubic Function

Consider the non-linear expression defined by the function:

$$f(x) = x^3 - 6x^2 + 9x$$

To find the $x$-coordinate of the point where the function has a local maximum, determine the critical points by first finding the derivative of the function and then solving for $x$ where the derivative equals zero.

Provide your answer as a simplified decimal or fraction.