微分中值定理的另类证明与推广

通常教科书中,微分中值定理的证明建立在罗尔(Rolle)定理之上.本文以实数连续性中的重要定理———区间套定理为依据,给出了拉格朗日微分中值定理的另类证明.此外,还给出了中值定理的若干推广形式.

The Different Proof and Spread of the Mean Value Theorem

In the general textbooks,the proof of the differential mean value theorem is built on the Rolle' Theorem.This paper is based on the Theorem of which is very important in the continuity of the system of real numbers.Also it gives a different way of proving the Lagrange Mean Value Theorem.Besides it draws several generalizing forms of the Mean Value Theorem.