For

$\displaystyle f(x)= \begin{cases}x^2,&\quad \textrm{x is rational}\\x^3,&\quad \textrm{x irrational}\end{cases}$

I want to know where $\displaystyle f$ is differentiable/not differentiable. I know it is differentiable at $\displaystyle x=0$.. but I kind of cheated and used the Squeeze Theorem to prove that.

I now want to that to show that $\displaystyle f$ isnotdifferentiable at the only other point where it is continuous, i.e. at $\displaystyle x=1$. I don't know how to show it explicitly in limit form, however.

Any help or tips are appreciated - thanks in advance!