分段函数在分界点处导数的一种求法  

A method of finding derivatives of piecewise function in division-point

作　　者：李胜正[1] 孙作胜[1] 房毅宪[1] 

机构地区：[1]山东轻工业学院数理学院,山东济南250353

出　　处：《山东轻工业学院学报（自然科学版）》2008年第4期69-71,74,共4页Journal of Shandong Polytechnic University

摘　　要：分段函数在分界点处的导数的计算,一般都要求用左、右导数定义及可导的充要条件去判定,本文讨论了分段函数在分界点连续的前提下,也可利用分界点左、右邻域内导函数的左、右极限是否存在且相等来判定,在一定条件下使求导运算更加快捷方便,并从几何上给出了进一步的阐述。The calculation of derivatives for piecewise function in division - point is commonly judged by a suf- ficient and necessary condition which left- right derivative can be defined and its derivative can be found. In this paper, it is discussed that piecewise function can also be judged by left - right limit of derived function in division- point＇s left - right field existing even being equal or not if it is continuous in division - point. It makes the calculation of derivative faster and more, convenient in a certain condition. And farther expatiation is presented in geometry.

关 键 词：分段函数 分界点 连续 左、右极限 左、右导数 

分 类 号：O172.1[理学—数学]