对称导数在研究函数上的应用  

Applications of Symmetry Derivative in Function Studies

作　　者：高静华[1] 梁波[1] 

机构地区：[1]大连交通大学理学院,辽宁大连116028

出　　处：《长春大学学报》2012年第12期1488-1489,1494,共3页Journal of Changchun University

基　　金：辽宁省教育厅高校科研项目(L2010075);吉林省教育科学"十二五"规划课题(GH12052)

摘　　要：导数在研究函数的单调性及极值问题上有重要价值。本文利用对称导数的定义、性质及中值定理,研究函数的单调性和极值等问题。结果表明:对称导数为正(负)时,函数是单调增(减)的。对称导数为零时,为极值点,二阶导大于零时为极小值,小于零时为极大值。Derivative has important value for studying the monotonicity and extremum of function. This paper studies monotonicity and extremum of function by applying the definition, property and mid-value theorem of symmetric derivative. The results show that the function is increasing（decreasing） if the symmetric derivative is positive（negative） and the symmetric derivative is zero in the extremum point. The second order symmetric derivative is positive in the rain-extreme value point, while the second order symmetric derivative is negative in max-extreme value Doint.

关 键 词：对称导数 单调性 极值 

分 类 号：O174[理学—数学]