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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