关于微分中值ξ的注记

A Note of Differential Mean Value

本文讨论了微分中值ξ的可导性与单调性。结果:如果f(x)在[a,b]上连续,在[a,b]内具有二阶连续导数,且f″(x)≠0,则ξ(x)在(a,b)内可导,并且若f″(x)不变号,则ξ(x)单调增加。

This paper discusses the derivatiability and monotonicity of differential mean value ? The results; if f(x) is continuous on Ca,b] and there is second order continuous derivative in (a,b), and f'(x)=0, then () is derivatiable; and if f'(x)>0 (or<0), then (x) is monotone increasing.