拉格朗日中值定理的几种证明  

Several Prove Lagrange Mean Value Theorem

作　　者：杨雄[1] 

机构地区：[1]娄底职业技术学院,湖南娄底417000

出　　处：《阴山学刊（自然科学版）》2017年第1期30-32,共3页Yinshan Academic Journal(Natural Science Edition)

摘　　要：拉格朗日中值定理在微分学中占有重要的地位,在解决函数增量与导数关系的一类问题中显得非常有效.为了更深入的理解Lagrange中值定理,文章从构造函数、三角形面积、坐标转换、引入行列式、引入区间套等方法给出了定理的证明;进而有助于拓宽思路,提升对定理的理解和应用,改善教学的效果.The Lagrange mean value theorem plays an important role in the differential calculus,which is very useful in solving the problem of the relation between the increment of the function and the derivative. We give the proof of the theorem by means of the method of the function,the triangle area,the coordinate transformation,the introduction of the determinant and the interval sets. These proofs help to improve students＇ understanding and application of the theorem,and improve the teaching effect.

关 键 词：拉格朗日定理 辅助函数 三角形面积 坐标转换 区间套 

分 类 号：O172.1[理学—数学]