Last edited by hbghlyj 2025-5-16 04:28$$
\lim_{x\to\infty}f(x)=L_0\quad\text{and}\quad\lim_{x\to\infty}f'(x)=L_1
$$
then necessarily $L_1=0$. The argument uses the Mean Value Theorem on the intervals $[n,n+1]$ and passes to limits along a suitable sequence.
