If $-x^2 \leq f(x) \leq x^2$ for all $x \in R$, prove that f is differentiable. If $-x^2 \leq f(x) \leq x^2$ for all $x \in R$ prove that f is differentiable.
I have found this link here for differentiability at 0, but what about the rest of the proof? Any ideas will be appreciated.
EDIT: 
Here is the link:
Prove that if $|f(x)| \leq x^2$, then the function is continuous and differentiable at $x=0$.

It is only true at $x=0$
You can make a zig zag between $x^2$ and $-x^2$ Which is not differentiable. 
