几个微分中值定理之异同——从罗尔定理到泰勒定理

Differences and Similarities in Several Differential Mean Value Theorem——from Roll Theorem to Taylor Theorem

要深刻地了解函数的性质,就必须进一步研究可导函数与其导数之间的关系.微分中值定理就深刻地揭示了它们的内在联系.微分中值定理是微分学教学的重点和难点.从理论上、形式结构上、定理的证明上等方面分析了几个微分中值定理的异同,揭示了微分中值定理在微分学中的重要地位和理论价值.

To have a deeper understanding of the nature of function, it is necessary to further study the relationship between function （assumed to be derivable） and derivative. Differential mean value theorem profoundly reveals the inherent relationship between them. The differential mean value theorem is the focus and difficult of the differential calculus. In theory, modality structure, and demonstration of theorem, this paper analyses the differences of these theorems, at the same time this paper reveals the important status and theoretical value of mean value theorem in differential calculus.