[…] A previous article describes how to use SAS to find the inflection points of a 1-D function that you can evaluate at any point. The function must be given by a formula (or by an algorithm) because the root-finding algorithm needs to evaluate the function at arbitrary locations. However, sometimes a function is known only at a finite set of points. This situation arises frequently in statistics. For example, a nonparametric regression curve does not have a simple closed-form expression. Neither does a nonparametric density function. Although these functions do not have an explicit formula, you can still use techniques from numerical analysis to approximate points where the first or second derivative of the function vanishes. …