6. Differentiability and Cusps

This section requires you to understand where functions are differentiable. For a function to be differentiable, it must first be continuous. If a function is continuous on a given interval, you need to look for where cusps may exist. Cusps are instantaneous changes in acceleration.

Obvious examples of cusps include:

Piecewise functions where the values on the edges of the intervals don't match.

Absolute value functions.