柯西与微分中值定理

Cauchy and the mean value theorem of derivative

目的考察柯西微分中值定理的证明,分析其中存在的问题。方法文献考证和历史分析。结果柯西的证明存在两个主要问题。结论通过对柯西关于微分中值定理证明的考察,分析其中存在的问题,对理解连续与一致连续,收敛与一致收敛概念有重要价值。

Aim To study Cauchy′s proof of the mean value theorem of derivative,analyze some problems in this proof,and propose some suggestions in teaching the mean value theorem of derivative.Methods Using the method of detailed literature investigation and historical analysis.Results Cauchy′s proof has two problems.Conclusion Through investigation and analysis,it is found that Cauchy′s work has important value in understanding continuity and uniform continuity,convergence and uniform convergence.