# Derivative Relationships

- Author:
- Mark Bethune

- Topic:
- Calculus, Derivative, Function Graph

This applet will help you to understand the relationships between the function and its derivatives.

1. Manipulate the sliders to observe how the graph changes shape. In particular, observe where the graph increases and decreases and where the concavity changes.
2. Sketch the graph of the first derivative on a separate sheet of graph paper. Check your answer by clicking the appropriate box.
3. Sketch the graph of the second derivative on the same set of axes and check your answer.
4. Deselect the boxes, manipulate the sliders and repeat the exercise.