分类：教育/科学-学习帮助
问题：若F(X)为偶函数,且F'(0)存在,证明F'(0)=0 
回答：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