Consider the following equation: $$f'(a)=\lim_{h\rightarrow 0}\frac{f(a+h)-f(a)}{h}$$

Let $f(x)=\sqrt[3]x$

If $a\ne 0$, use the above formula to find $f'(a) =$

Show that $f'(0)$ does not exist and that f has a vertical tangent line at (0,0)