对Lagrange中值定理证明方法的讨论

Some New Proofs of the Lagrange Mean Value Theorem

对Lagrange中值定理的证明,在高等数学的传统证法中,通常都是采用引入一个“辅助函数”,将适合定理的函数转换成适合Rolle中值定理的函数的办法.本文给出了行列式证法、旋转变换证法和区间套定理证法等几种证明方法.

In Calculus, the standard proof of the lagrange Mean Value Theoremis is to introduce an auxiliary function so as to transform the eriginal fanction into a new one on which one can apply the Rolle Meam Value Theorem. In order to understand the Lagrange Mean Value Theorem better, we provide three new proofs in this paper by using 1) determinonts, 2) kotatrons and transformations, and 3) principle of Nested Intervals, respectively.