罗尔定理的推广及其应用  

Promotion of Rolle Theorem and it's application

作　　者：赵凌燕[1] 李宝毅[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2016年第4期6-9,共4页Journal of Tianjin Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11271046);天津师范大学博士基金资助项目(52XB1414)

摘　　要：基于罗尔定理,研究2种函数零点个数上界的问题.对于第1种函数,利用导函数的性质确定了不含间断点的函数零点个数的上界,进而确定了含间断点的函数零点个数的上界.对于第2种函数,利用函数满足的微分方程的特征确定了函数零点个数的上界.On the basis of Rolle Theorem, the upper bounds of numbers of zeros for two kinds of functions are studied. For the first kind, the upper bound of zeros for the functions without discontinuities is determined by using the properties of derived functions, and then the upper bound of zeros for the functions with discontinuities is given. For the second kind, the upper bound of zeros is determined by using the features of the differential equation for the functions.

关 键 词：罗尔定理 零点个数 零点重数 间断点 

分 类 号：O175.1[理学—数学]