Problem 737 (difficulty: 5/10)

Assume that \(\displaystyle f\in C^{\infty}(0,\infty)\), \(\displaystyle \lim_{0+0}f=\lim_{\infty} f=0\). Prove that \(\displaystyle \exists \xi>0\): \(\displaystyle f^{''}(\xi)=0\).

Give me another random problem!