设函数<img src="https://static.zxtiku.com/wangke/imgs/topic/e817c5560a9e362d8bae0ff1f8763331.png"/>在<img src="https://static.zxtiku.com/wangke/imgs/topic/06df24857cec9240ca2f12e9d3a59517.png"/>连续，在<img src="https://static.zxtiku.com/wangke/imgs/topic/02c4eaadfbbde9b24c67cbb15b94e843.png"/>内可导，且<img src="https://static.zxtiku.com/wangke/imgs/topic/5a6a3c7df7b5e309228209aff4d2d3e1.png"/>，证明：在<img src="https://static.zxtiku.com/wangke/imgs/topic/02c4eaadfbbde9b24c67cbb15b94e843.png"/>内至少存在一点<img src="https://static.zxtiku.com/wangke/imgs/topic/91cf9e5446c0593a258fc4ae394450c8.png"/>，使得<img src="https://static.zxtiku.com/wangke/imgs/topic/043aa8de7bad086fa4aafc77ff049c5e.png"/>成立时可构造辅助函数<img src="https://static.zxtiku.com/wangke/imgs/topic/d104aafb3ffee516d58098342258b115.png"/>