$\mathop {\lim }\limits_{x \to \infty } f\left( x \right) = L$ Prove $\mathop {\lim }\limits_{x \to \infty } f'\left( x \right) = 0$
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