[例5]设f(x )在[0,1]上连续,在(0,1)内可导,且 f(0)=0 (1)=1, 试证对任意-|||-给定的正数a,b,在(0,1)内一定存在互不相同的ξ,7使-|||-dfrac (a)(f'(xi ))+dfrac (b)(f'(n))=a+b.