浅析多元函数的极值摘要 函数的极值不仅在实际问题中有重要应用，而且也是函数性态的一个重要特征.本文首先了讨论一元函数极值定义、性质及判定，分析求函数极值的方法和依据.其次，从二元函数极值的定义、性质出发，对多元函数极值的求法进行讨论，总结多元函数极值的常用求法，如拉格朗日乘数法、代入消元法，并分别讨论这几种方法在应用时的注意事项，接着讨论多元函数的条件极值，着重讨论如何将其转化无条件极值问题，最后总结了多元函数极值的几种应用，如函数极值在考研数学、证明不等式、物理学中的应用，从而证明多元函数极值应用的广泛性，并给出相应的结论，以期对学习极值有助力.关键词 多元连续函数 极值 条件极值 无条件极值 拉格朗日乘数法Analysis of extreme value of multivariate functionAbsract The extremum of function is not only an important application in practical problems, but also an important characteristic of function behavior. In this paper, the definition, properties and judgement of extreme value of function are discussed. Secondly, starting from the definition and properties of the extremum of the function of two variables, the paper discusses the method of finding the extremum of the function of many variables, and sums up the common methods of finding the extremum of the function of many variables, such as the Lagrange multiplier method, the substitution elimination method, then, it discusses the conditional extremum of multivariate function, especially how to transform it into unconditional extremum, finally, it summarizes several applications of the extremum of multivariate function, for example, the application of function extremum in mathematics, inequality and physics is proved, which proves the extensiveness of the application of multivariate function extremum, and gives the corresponding conclusion, so as to be helpful to study extremum.Key words Multivariate continuous function Extreme value Conditional...
