Check for what $n\in\mathbb{N}\cup \left\{+\infty\right\}$ $f\in C^n(\mathbb{R})$ (that is $f$ is $n$ times differentiable, I wasn't sure that this designation is common), if:
a) $f(x)=|x|^m, \ m\in\mathbb{R}$
b) $f(x)= \begin{cases} e^{-1/x}, \ x>0 \\ 0, \ x\le 0 \end{cases} $
I wasn't given in school any convenient theorem to check such things but I really want to learn it. How can I check it?