1. The problem is to find the critical points of a function. 2. Critical points occur where the derivative of the function is zero or undefined. 3. The general steps are: - Find the derivative $f'(x)$ of the function $f(x)$. - Solve the equation $f'(x) = 0$ to find potential critical points. - Check where $f'(x)$ is undefined, as these points can also be critical. 4. Example: For $f(x) = x^3 - 3x^2 + 4$, find $f'(x) = 3x^2 - 6x$. 5. Set $3x^2 - 6x = 0$ and factor: $3x(x - 2) = 0$. 6. Solve for $x$: $x = 0$ or $x = 2$. 7. These $x$ values are the critical points of $f(x)$. 8. Always verify if the derivative exists at these points and consider the domain of the function.