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.为了进一步开阔思路,更好地理解和掌握Lagrange中值定理,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 Theorem is to introduce an auxiliary function so as to transform the original function into a new one which can apply the Rolle Mean Value Theorem.In order to understand the Lagrange Mean Value Theorem better,this paper provides three new proofs by using deter-minants,rotations and transformations,and Principle of Nested Intervals respectively.