# Math Insight

### Overview of: The derivative, critical points, and graphing

Finding the critical points of a function is useful for sketching its graph. Since critical points are the only places where the derivative can change sign, the function cannot change between increasing and decreasing except at a critical point. For each interval between critical points, one needs only check the sign of the derivative at one point to determine the behavior of the function in the entire interval.

Total points: 3