令F(x)=f(x)-f(a)-(x-a)f'(x)G(x)=g(x)-g(a)-(x-a)g'(x)对F(x),G(x)在[a,b]上用柯西定理.F(b)-F(a)就是等式左边分子，G(b)-G(a)就是等式左边分母F'(s)=f'(s)-f'(s)+af''(s)=af''(s)G'(s)=g'(s)-g'(s)+ag''(s)=ag''(s)代入柯西定理即得右边。
