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 ...

In the study of production scheduling to meet random fluctuations in supply and demand, a probabilistic measure of effectiveness can be used. This measure is a piecewise quadratic positive definite ...

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.