Overview:

One of the ways to visually think of the derivative is to use the idea of local linearity. That is, if you look “up close” at the graph of a differentiable function, it appears almost straight, so locally (on a small enough interval) a differentiable function behaves very much like a linear function.

You can experience this directly by using a graphing handheld. If you zoom in repeatedly on a particular point on the graph of a differentiable function, eventually the graph appears indistinguishable from a straight line. The slope of that line is the value of the derivative at that point.

Materials:

• TI-84 Plus / TI-83 Plus
• Graph paper

Activity:

Introduction to Slope Fields