Finding Local Maximum of a Polynomial Function

Consider the function defined by the equation:

$$f(x) = 2x^3 - 3x^2 + 4$$

We want to find the x-coordinate of the local maximum of this function. To determine the local extrema, we need to find the critical points of the function by taking its derivative, setting it to zero, and solving for $x$. What is the x-coordinate of the local maximum?