[Everyday Mathematics]20150120

设 $f:\bbR\to\bbR$ 二阶可微, 且 $$\bex f(0)=2,\quad f'(0)=-2,\quad f(1)=1. \eex$$ 试证: $$\bex \exists\ \xi\in (0,1),\st f(\xi)\cdot f'(\xi)+f''(\xi)=0. \eex$$