As homework we were given 2 questions:
Find a function that is continuous at exactly one point and not differentiable there.
Find a function that is differentiable at exactly two points.
The answer to the first one was somewhat simple - $ f(x) = x*D(x) $, wherein $ D(x) $ stands for Dirichlet function.
I've been thinking about the second question for a while, and someone suggested me the following: $ g(x) = x^2*D(x) $
$ f(x) = (x-1)^2 * g(x) $
Claiming that $f(x)$ is only differentiable in $ x = 0, x = 1 $. Why is that?