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.

In this problem, the optimal path is one that maximizes the expected utility, with the utility function being piecewise-linear and concave. Such a utility function can be used to approximate nonlinear ...

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 ...