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 hard way.

By that I mean they will pick a number in each interval between the critical points and then substitute it into the derivative and do a lot of arithmetic to determine whether the derivative is positive or negative. Arithmetic is not necessary, when all you really need is the sign of the derivative. The method I suggest is easier and involves no arithmetic and therefore precludes any arithmetic mistakes

A complete discussion of this idea with examples click here or look on my Resources page.