1. **Stating the problem:** We want to find the critical points of a function, which are points where the function's slope is zero or undefined. 2. **Formula and rules:** Critical points occur where the first derivative $f'(x)$ is zero or does not exist. 3. **Step-by-step process:** - Find the first 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. **Explanation:** Critical points are important because they indicate where the function may have local maxima, minima, or points of inflection. 5. **Example:** For $f(x) = x^2 - 4x + 3$, - Compute $f'(x) = 2x - 4$. - Set $2x - 4 = 0$ which gives $x = 2$. - Since $f'(x)$ is defined everywhere, the only critical point is at $x=2$. 6. **Summary:** To find critical points, always find where the derivative is zero or undefined, then analyze those points further if needed.