Suppose that the function $\displaystyle g: \mathbb {R} \rightarrow \mathbb {R} $ is differentiable at $\displaystyle x_0=0$. Also, suppose that for each natural number n, $\displaystyle g( \frac {1}{n} ) = 0$. Prove that $\displaystyle g(0)=g'(0)=0$

I really don't know how to start this one, please give me some hints, thanks!