finite $\lim_{x \rightarrow +\infty} f(x)$ and $\lim_{x \rightarrow +\infty} f'(x)$. Then $\lim_{x \rightarrow +\infty} f'(x) = 0$
Proving that $\lim\limits_{x\to\infty}f'(x) = 0$ when $\lim\limits_{x\to\infty}f(x)$ and $\lim\limits_{x\to\infty}f'(x)$ exist