A continuous function is 'mostly' nowhere differentiable

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About this postIt is taught in elementary calculus course that, if a function is differentiable at some point $x_0$, then it’s continuous at $x_0$, but not vice versa. It’s easy to construct an counterexample which is continuous but not differentiable. An example is $y=|x|$ at $x=0$. In fact, we can……