关于中值定理的注记

Notes on Mean Value Theorems

举例说明了人们普遍接受的说法“通过函数图形旋转可以应用罗尔定理来证明拉格朗日中值定理”是错误的;并证明柯西中值定理实际上是参数方程形式的拉格朗日中值定理;最后重申拉格朗日中值定理的一个重要推论(导数极限定理)并说明其在相关问题求解中的应用.

It is illustrated by examples that the commonly accepted parlance that Lagrange s mean value theorem can be derived from Rolle s theorem by means of a rotation of the function figure is wrong.It is also demonstrated that the Cauchy s mean value theorem is actually the Lagrange s mean value theorem in parameter equation form.Finally the derivative limit theorem is reasserted and its applications to solutions of related problems are explained.