分段函数可导性的教学探析

Teaching Analysis on the Derivability of Piecewise Function

分段函数的分界点的导数是高数学习难点问题之一,通过对分段函数分界点是否可导进行分析,并应用实例给出判断的具体计算过程。然后探索了若分界点左(右)导数存在,则此左(右)导数与左(右)导数极限有何关系,进而得出一结论,并应用结论求解分界点的导数值。

The derivative of the demarcation point of a piecewise function is one of the difficult problems in advanced mathematics.By analyzing the differentiable points of the piecewise function,the specific calculation process of the judgment is given by an example.The relationship between the left（right）derivative and the left（right）derivative limit is explored if the left（right）derivative exists in the boundary point.Then a conclusion is drawn and the derivative value of the demarcation point is solved by the application of the conclusion.