 # 保持共产党员先进性教育心得体会(三十七)

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