Suppose $f:\rightarrow$ to R and has continuous $f'(x)$ and $f''(x)$ f(x) → 0 as x → ∞. Show that f′(x)→0 as x→∞

Suppose $f:[0,\infty)$ $\rightarrow$ R and has continuous $f'(x)$ and $f”(x) $ .

$f(x) $$\rightarrow $0 as $x$ $\rightarrow$ $\infty$. Given $f'(x)\rightarrow b$ as $x \rightarrow \infty$

show that $b=0$

Get stuck in the first place, but I tried to use Mean Value Theorem and then connected it to the limits.

Any hint?

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