设f(x)在【0,1】上连续,且f(0)=f(1).证明:一定存在Xo∈【0,1/2】,使f(Xo)=f(Xo+1/2)

问题描述:

设f(x)在【0,1】上连续,且f(0)=f(1).证明:一定存在Xo∈【0,1/2】,使f(Xo)=f(Xo+1/2)

考虑辅助函数g(x)=f(x)-f(x+1/2),0