关于二元函数极值判别中判别式为零时的几个讨论

Discussion on the Extreme Value of Functions of Two Variables When the Discriminant Is Zero

摘要: 本文主要讨论了多元函数在驻点处利用充分定理判别极值失效时的一些问题，借用一元函数或二元泰勒公式进行推广探讨极值的存在性，并利用结论解决一些实例。

Abstract: The second derivative test for local extreme values of a function with two variables may be inconclusive. In this paper, the author mainly considers above case and discusses the existence of local extremum based on univariate functions and Taylor’s formula for functions of two variables. According to the conclusion of this paper, the author also analyzes the behavior of several specific functions at the stationary point.