柯西(Cauchy)中值定理又称一般中值定理.本文给出关于这个定理的一个有别于一般证法的矢量法证明,并给出它在三维空间矢量分析中的一个推广。柯西中值定理设函数f(t)、F(t)在闭区间[a,b]上连续,f′(f)、F′(t)在开区间(a,b)内存在,且F′(t)在(a,b)内每一点均不为零,则存在一点§∈(a,b),使得 Cauchy’s mean value theorem is also called the general mean value theorem. This paper gives a vector method proof which is different from the general proof method of this theorem, and gives a generalization of it in 3D space vector analysis. Cauchy’s mean value theorem allows functions f(t) and F(t) to be continuous in the closed interval [a,b], and f’(f), F’(t) exist in the open interval (a,b), and F’ (t) If every point in (a,b) is not zero, then there is a little §∈(a,b) so that