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.

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 ...

Dimitris Bertsimas, David Gamarnik, John N. Tsitsiklis, Performance of Multiclass Markovian Queueing Networks via Piecewise Linear Lyapunov Functions, The Annals of Applied Probability, Vol. 11, No. 4 ...