若F(X)为偶函数,且F'(0)存在,证明F'(0)=0
F'(0) =lim(F(h+0)-F(0))/(h-0) h趋于0 =lim(F(h)-F(0))/h h趋于0 =-lim(F(-h)-F(0))/(-h) h趋于0 =-lim(F(-h+0)-F(0))/(-h-0) -h趋于0(=h趋于0) =-F'(0) 2F'(0)=0 F'(0)=0