f(x)在[x1,x2]可导,x1x2>0证明存在ξ ∈ (x1,x2)使〔x1f(x2)-x2f(x1)〕/（x1-x2）=f(ξ )-ξ f’(ξ )
问题描述：
f(x)在[x1,x2]可导,x1x2>0证明存在ξ ∈ (x1,x2)使〔x1f(x2)-x2f(x1)〕/（x1-x2）=f(ξ )-ξ f’(ξ )
答
构造函数g(x)=f(x)/x,h(x)=1/x因为x1x2>0,所以x1≠0,x2≠0,所以g(x),h(x)在[x1,x2]连续,在(x1,x2)可导,且h'(x)≠0,满足柯西中值定理条件,由柯西中值定理有：[g(x1)-g(x2)]/[h(x1)-h(x2)]=g'(ξ)/h'(ξ)（以下为整理...