finite $\lim_{x \rightarrow +\infty} f(x)$ and $\lim_{x \rightarrow +\infty} f'(x)$. Then $\lim_{x \rightarrow +\infty} f'(x) = 0$

Question

Let f be twice differentiable function on R with finite $\lim_{x \rightarrow +\infty} f(x)$ and $\lim_{x \rightarrow +\infty} f'(x)$. Then $\lim_{x \rightarrow +\infty} f'(x) = 0$

I don't know how to prove this.