幂函数x~α在微分中值公式中的中值点的位置

The Position of the Midpoint of the Power Function x~α in the Differentiation Median Formula

本文就α>2的情形,对幂函数x~α在一类区间上的Lagrange微分中值公式中的中值点ξ的位置作出估计,并在此基础上得到幂函数x^a(α>2)在区间[a、b](0<a<b)上的微分中值公式的中值点ξ满足(a+b)/2<ξ<b的结论。

The article estimates the midpoint of the power function xα in the category one of the mean value theorem of Lagrange on condition of α>2, and thus concludes the mid-point 5 of power function xα(α>2) satisfies a+b/2<ξ<b in the mean value theorem in the zone [a,b](0<a<b).