Let (piece wise function) f(x)= x^(1/3), for x=/= 0; 0 for x=0.
So is this function differentiable at x=0? Could you explain why or why not? Thanks!
The function differentiable at $\displaystyle x=0$ iff the limit $\displaystyle \lim_{h\to 0}\frac{f(h)-f(0)}{h}$ exists. But $\displaystyle \lim_{h\to 0}\frac{f(h)-f(0)}{h}=\lim_{h\to 0}\frac{h^\frac{1}{3}-0}{h}=\lim_{h\to 0}h^{-\frac{2}{3}}$, so the limit doesn't exist.