f(x)是偶函数,
∴f(-h)=f(h),
又f'(0)存在,
∴h→0+时[f(h)-f(0)]/h与[f(-h)-f(0)]/(-h)的极限都存在且等于f'(0),
[f(h)-f(0)]/h+[f(-h)-f(0)]/(-h)=0,
∴2f'(0)=0,
f'(0)=0.