Question

Can a function be continuous and non-differentiable on a given domain?

Answer 1

Yes

Explanation:

While most calculus students will likely be familiar with functions that are continuous but not differentiable at specific points (e.g. `f(x) = |x|` is continuous but not differentiable at `x=0`), there are also functions which have that property over larger domains. For example, the Weierstrass function is continuous on all of `RR`, but is not differentiable at any point.