Prove or disprove: If $I$ is a neighborhood of $x_{0}$ $\in$ $\mathbb{R}$ and $f\colon I\to \mathbb{R}$ is differentiable at $x_{0}$ then $f$ is differentiable for at least one other $x$-value in $I$.
I am really lost with this one. I think it's true but I can't go any further. Could someone please help me out?
For a counter example consider $f(x)=x^2$ if $x$ is rational and $f(x)= -x^2$ if $x$ is not rational.
Note that f(x) is differentiable only at $x=0$