分段函数在分段点处可导性与连续性的判定方法

Determination Method of Piecewise Function Differentiability and Continuity in Piecewise Point

连续性与可导性的判定是高职学院高等数学课程非常重要的一部分内容,分段函数作为一类比较常见的函数,对学生后续专业课程及岗位实践工作都有着非常重要的作用。分段函数可导性与连续性的学习是高等数学课程教学的重点,也是难点所在。通过两种类型的分段函数的连续性与可导性的讨论方法,给出高职学院学生在这部分内容的学习中应掌握的方法,连续性与可导性的应用可以解决高职学院高等数学很多相关问题,有比较高的实用价值。

Continuity and derivative of judgment is a very important part of advanced mathematics in higher vocational colleges. As one of the more common functions, piecewise function plays a very important role on their following professional courses and practice post work. The guided and continuous learning of Piecewise function is not only the focus but also a difficulty of higher mathematics teaching. Through continuous piecewise function of two types of differentiability and discussion method, this paper emphasizes that the vocational college students should master the method in this part of the contents. The continuity and differentiability of the application＇ of higher mathematics in higher vocational college can solve many related problems and have a high practical value.