微分中值定理证明中辅助函数的构造

The construction of additive functions to testify differential mean value theorem

由复数x+yi与直角坐标平面上的点(x,y)(x,y∈R)的一一对应关系,将复平面与直角坐标平面看成是一致的,通过复数乘法运算构造出一系列拉格朗日中值定理证明中满足罗尔中值定理条件的辅助函数,并明确指出了柯西中值定理证明中辅助函数的构造方法.

According to the one-to-one correspondence between the complex numberx＋ yi and the point （x, y）（x, y∈R） on the plane, can take them as identical. Constructed a series of additive functions to meet Rolle theorem conditions with the multiply method of complex numbers while testifying Lagrange mean value theorem, also put forward a method of constructing additive functions to testify Cauchy mean value theorem.