RE: Functions that are NOT Differentiable

Yeah, and there are also functions everywhere continous and nowhere differentiable. But their graphs are very complicated to draw

There are also functions everywhere differentiable but not monotone on ANY interval (a, b). They are even strangest.

Multivariate functions can be differentiable in Frechet sense but not in Gatoux sense.

And there are complex functions which are differentiable in weaker Real sense but not in stronger Complex sense.

Analysis is full of beautiful things.