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根据初等数学中的有关极值问题的类型及相应的解法 ,结合微积分中有关极值问题的知识 ,提供了比较切合中学数学教学的 2种解题模式。模式 1提出了等值线概念 ,利用等值线与给定动点路径的关系来确定在已知路径上获得极值的方法。模式 2利用多变量函数取得极值的必要条件 ,通过暂时固定某些可变量 ,将多变量函数的极值问题转化为单变量或二变量函数等的局部极值问题
According to the types of elementary problems in elementary mathematics and the corresponding solutions, combined with the knowledge about the extremum problems in calculus, we provide two kinds of problem solving modes which are more suitable for the teaching of middle school mathematics. Pattern 1 proposes the notion of contour and uses the relationship between the contour and the path of a given moving point to determine the method of obtaining the extremum on the known path. In model 2, the necessary conditions for obtaining extremums by multivariable functions are obtained. By exchanging certain variables temporarily, the extremum problems of multivariable functions are transformed into the local extremum problems such as univariate or bivariate functions