【摘要】 Rolle定理和Lagarange定理是两个重要的微分中值定理,它们是Cauchy定理的基础,进一步为L’Hospital法则求极限提供了理论依据.它们还是研究函数增减性、凹凸性的基础.它在整个微分学中起着把微分的概念和方法应用于许多数学物理问题的桥梁作用.本文用区间套定理给出它的另一种证明.更多还原

【Abstract】 Rolle theorem and Lagrange theorem are two important theorems in the calculus,they are the base of the Canchy theorem, and they provide theoretic basis for L’Hospital rules to calculating limit, they are also the basis for analyzing function increase and decrease or concavity-convexity. They play an important roll in putting the calculus principle and method into the use of mathematical and physical equation.In this essay, the author reproves them with nestal Interval theorem.更多还原