有关中值定理中间点位置的两个定理

Two Theorems Concerning the Position of the Intermediate Point of Median Theorem

对于∪+∞i=1[ai,ai+1)=[0,+∞),aiai+1=I(I可为任意确定的正数),i=1,2,…,给出了一类单调函数u(x),x>0在区间[ai,ai+1],i=1,2,…的拉格朗日中值定理中间点(设为ξi,i=1,2,…)的位置随i值单增而变化的规律。并且对于函数u(x)在任意区间内的中间点的位置给出了一个上界。

In this paper,for U+∞i=1[a_i,a_(i+1)]=(0,+∞),(a_ia)_(i+1)=I,i=1,2,…,(I can be any determined positive number),we give the law that,for the position of langrange mean point(let it be ξ_i i=1,2,…)of function u(x),x>0 vary mono-increasingly with the value of i on [a_i,a_(i+1)],and an upper limit of (a_i,ξ)_(i).