# Math Help - Is this function differentiable?

1. ## Is this function differentiable?

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!

2. The function differentiable at $x=0$ iff the limit $\lim_{h\to 0}\frac{f(h)-f(0)}{h}$ exists. But $\lim_{h\to 0}\frac{f(h)-f(0)}{h}=\lim_{h\to 0}\frac{h^\frac{1}{3}-0}{h}=\lim_{h\to 0}h^{-\frac{2}{3}}$, so the limit doesn't exist.