Building a Function with Conditions on f, f', f"

In the App

This activity was written by Tim Brzezinski. (Dr. Jackson only turned on the labels on the points and added the text.) It investigates your knowledge of the relationships among the original function and its first and second derivatives. Move the white points to make a quadratic function meeting the given criteria. When you think you have it click on Check Graph. Click on New Problem to try it with different criteria.

First Derivative and Graph of Original Function

What does the sign of the first derivative tell us about the shape of the original graph? (Be as specific as possible.)

Second Derivatie and Graph of Original Function

What does the sign of the second derivative tell us about the shape of the original graph? (Be specific.)