If $\lim\limits_{x \to \infty} f(x)$ is a finite real number and $f''(x)$ is bounded, then $\lim\limits_{x \to \infty} f'(x) = 0$
If $f(x)\to 0$ as $x\to\infty$ and $f''$ is bounded, show that $f'(x)\to0$ as $x\to\infty$