|||
1.$f \in C [0,1]\mbox{且}f$在$(0,1)$上二阶可导,$f''(x)\neq 0$
$$\int_{0}^{1} f(t)\mbox{d}t=0, f(0)=f(1)>0$$
证明:(1)$f''(x)>0$ .
(2)$f(x)=0$在$(0,1)$上恰有两根.
(3)$\exists \xi \in (0,1),s.t.\quad f'(\xi)=\int_{\xi}^{1} f(t) \mbox{d} t$.
Archiver|手机版|科学网 ( 京ICP备07017567号-12 )
GMT+8, 2024-10-20 01:46
Powered by ScienceNet.cn
Copyright © 2007- 中国科学报社