The summer examination season sees pupils searching for maximums and minimums on their text papers.

This long-standing pursuit was initiated by the likes of Newton and Leibniz in their calculus.

It can be all too difficult to think about for some:

“our modern Analysts are not content to consider only the Differences of finite Quantities: they also consider the Differences of those Differences, and the Differences of the Differences of the first Differences. And so on ad infinitum.”

*Bishop Berkeley, The Analyst, 1734*

The example above is one in which Euler demonstrates the geometrical significance of the first and second derivatives.

Note that the Point of Inflection is where and is a change from upward to downward convex curvature, or vice versa. There is no need for too.