中值定理的一个新推广

A NEW EXTENSION OF THE MEAN VALUE THEOREM FOR DIFFERENTIAL

本文给出了Ｒｏｌｌｅ定理、Ｌａｇｒａｎｇｅ中值定理与Ｃａｕｃｈｙ中值定理的一个新的推广．

In this paper, We give a new extension of the Mean Value Theorems for differential, That is the following theorems :Theorem (The extension of Rolle's theorem)If f(x) is differential in (a ,b) , and there are two sequences of points {an}、{bn} in (a ,b) ,Such that am→a ,bn→b (n→∞), limf(an) = limf(bn)= A, Where a may be definite real number or -∞,b may be definite real number or + ∞,A may be definite real number or ±∞.Then, there is at least one point ∈(a ,b) ,at which f'= 0.Similary, We have extension of the Lagrange Mean Value Theorem and the extersion of the Cauchy Mean Value Theorem.