Seminar

The functions they don't tell you about in calculus

The functions we use in a calculus class are typically very well behaved.  So much so that we get used to not checking hypotheses before applying a theorem.   For instance, when using Taylor's Theorem, when was the last time you had to check that a function was $n$-times differentiable?  We usually work with the likes of $e^x$, $\cos x$, and $\sin x$, which can be differentiated over and over without ever stopping.  In fact, without googling, could you give an example of a function that can \textit{only} be differentiated \textbf{twice} at a point?