函数极值问题

函数极值问题
 

摘要：这篇主要讨论了函数的极值问题，包括1元函数极值，2元函数极值，多元函数极值，以及条件极值拉格朗日方法等，在讨论的过程中从温了书本上的定理，比如：罗尔定理，柯西定理，泰勒定理，拉格朗日中值定理等。也能应用函数极值问题中所学到的定理和方法解决实际问题，解决最大值和最小值的应用问题，判断函数的增减性与函数图形的凹凸性、求函数图形的拐点等方法等；更主要的对书中的定理进行升华，推导和证明1些定理并推广，使定理能够1般化，加强自身的数学修为。

关键字：函数极值；1元函数；2元函数；多元函数；驻点；连续；极大值；极小值。

The problem of the functional extremum
 

Abstact ：This paper mainly discusses the problem of the functional extremum, including  the functional extremum of one variable,the functional extremum of two variables, the functional extremum of several variables, and extremum with a condition etc. In the process of discussing ,we review the axioms on the book, for example:Roll theorem,Cauchy theorem, Taylor theorem ,Lagrange mean value theorem etc..Also we can use the axioms and methods learning from the functional extremum to resolve the actual problem,such as resolving the applied problem of maximum value and minimum value, judging the monotone dependence of function ,looking for the character of cave and convex of the functional sketch and the methode to find the point of contrary flexure according to the functional sketch ect.But the principal purpose is that raising the theorem to a higher level,  deducing and proving some axiomses combined the expansion, making axioms generalized.At all we can strengthen the knowledge of mathematics .

Key word: functional extremum; function of one variable ;function of two variables ;function of several variables; stable point; consecution; maximum value,; minimum value

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