条件极值的充分条件与一类椭圆方程

通过分析无条件极值与条件极值的充分条件具有不同判别矩阵的原因,推导出条件极值充分条件的判别方法,得出其自变量增量间的关系式,得到了多维多约束状态下条件极值充分条件的一种更精确的判别矩阵,并举正反例说明判别驻点时可能出现的情况.有助于理解两种充分条件的关联及差别,提供了一种寻找更精确的条件极值充分条件的判别矩阵的方法.

On Sufficient Condition of Conditional Extreme Value and a Kind of Ellipse Equations

There is rarely discussion on sufficient condition of conditional extreme value of multi-variable function constraint to equalities in most mathematical analysis teaching materials, or with rather complex discussion instead, but conditional extreme value always follows unconditional extreme value tightly, which makes difficult to understand the relevance and difference between two kinds of discriminant matrices of sufficient conditions for students, or in mistake that both of discriminant matrices are in identity. To help students gasp the relevance and difference between both of them profoundly, understand sufficient condition of both problems of extreme value quicker and more comprehensive, sufficient conditions of unconditional and conditional extreme value have been discussed in detail, and different situations may encounter in distinguishing with various kinds of stationary points been explained by examples of validity and invalidity, this can help students understand the problem of extreme value quicker, more profoundly and comprehensively.