Need to prove $f(x)=0$ for all $x \in R$

Question

$f(x)$ is infinitely differentiable and $∃ L∈\mathbb{R}$ such that $|f^{(k)}(x)|≤L$ for any $k∈\mathbb{N}$.

I need to prove that :

If $f(1/n)=0$ then $f(x)=0$ for any $x∈\mathbb{R}$.