设F(x)在【0,1】上连续,在（0,1）内可导,且F（0)=F(1）=0,F(0.5)=1,试证至少有一点W,使F'(W)=1

设 G(x) = F(x) - x
G(0) = 0
G(1) = -1
G(0.5) = 0.5
所以 G(x) 的最大值必在开区间（0,1）中一点 w 达到.于是 G'(w) = 0,
即：F'(w) - 1 = 0 =====> F'(w) = 1