[eigenket]

> Does continuity implies differentiability? For almost all practical cases yes, but when you want to be general, thats when you get the Weierstrass function [1], a weird function

Ok I have to jump in and disagree with you. Non-differential continuous functions are far more ubiquitous (and useful) than you're suggesting here. The most obvious examples are the absolute value function and ReLU (rectified linear unit) activation function which turns up in a machine learning/neural network context.

I think you're thinking about being non-differentiable everywhere, but it's very easy to cook up examples of practically relevant functions which turn up to be non-differentiable somewhere.