摘要
讨论一个微分中值命题条件的弱化,将条件"f′(x)g′(x)>0"弱化为"f(a)≠f(b)",利用介值定理和柯西中值定理给出证明,以扩大命题的适用范围,并举出实例予以说明.
This paper provides a weaker condition for the differential mean value proposition. Instead of the condition f′（x）g′（x）〉0, we propose f（a）≠f（b） which is weaker. Our proof is based on the intermediate value theorem and Cauchy mean value theorem. Examples are also included.
出处
《高等数学研究》
2011年第5期25-26,共2页
Studies in College Mathematics
关键词
微分中值定理
介值定理
柯西中值定理
可导函数
differential mean value proposition
intermediate value theorem
Cauchy mean value theorem
differentiable function.
