函数在一点的可导性与在该点附近的导数的关系

The Relationship between the Differentiability on a Point of a Function and the Derivatives of the Function around the Point

本文通过研究函数在一点的可导性与函数在该点附近的导数的关系,得出了函数在一点可导的一个充要条件,并通过举例说明了它在研究分段函数在其分段点的可导性方面的运用。

In the paper, we discuss the relationship between the differentiability on a point of a function and the derivatives of the function around the point, and get a sufficient and necessary condition for the function to be differential on a point. There are some examples for the application of the differentiability of a piecewise function on its piecewise point.