If $f$ is a derivative of the interval $[0,+\infty)$ and $\lim\limits_{x\to+ \infty}:f(x)=L$ and $\lim\limits_{x\to +\infty}:f'(x)= A$ and $A$ , $L$ are real numbers, then $A=0$
Give an example of a function $f$ such that has a limit in $+\infty$ but $f'$ does not have a limit in $+\infty$.
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I'm thinking about constant functions but it's not true!
