But I argued that it would be more helpful to students’ understanding of the derivative to start with a simpler case first, namely to use only piecewise-linear functions at the beginning.

Move the point T along the graph of y=sin(x) by moving the slider. The slope function (derivative) is then traced out in blue. Can you identify the graph of the derivative? This is a Java Applet ...

Many data are suitably modeled by functions consisting of straight-line segments. These functions may be called piecewise-linear. Smooth functions that are related to the hyperbola and that have ...