Inequalities

This is an “extra” post on a technique that students are using a lot right now in graphing functions and working on optimization problems. In analyzing a derivative to find critical points and then the intervals where the function increases and decreases you need to solve these inequalities. I’ve observed many students solving inequalities the…

Joining the Pieces of a Graph

In this post we will consider how the shapes discussed in the previous two posts can join together. Continuity and the derivative at the point where two shapes join tell us what’s going on. Graphs can change from one shape to another only at places where: The first derivative changes sign. For this to happen,…