以中值定理为工具，给出了利用一阶偏导数判定二元函数极值的方法。
The criterion extreme value of binary function for first partial derivative is given by means of the mean value theorem. The two theorems are obtained.
将一元函数和二元函数极值的部分判别方法推广到多元函数极值的判别，提出了判定多元函数极值的几个方法。
The extreme conditions for the monovariate functions were applied to the multivariate functions and then an effective method to decide the extreme values for the multivariate functions was presented.
本文利用二次型理论给出了二次函数最值的一个充分条件及求法 ，定义了二元齐次多项式的正定性 ，并基于定义给出了二元函数极值的一个充分条件。
This paper is mainly devoted to provide a supplementary analysis of extreme value problem of bivariate functions, in which a new sufficient condition and its concise proof when critical case is given.
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