洛尔定理的2个推广形式  

Two Forms of the Extended Application of Rolle’s Theorem

作　　者：孙兰敏[1] 

机构地区：[1]衡水学院数学系,河北衡水053000

出　　处：《衡水学院学报》2005年第1期1-2,共2页Journal of Hengshui University

摘　　要：通过将洛尔定理中的条件“有限区间”推广到“任意区间”,证明了洛尔定理中的结论仍然成立;将洛尔定理中的条件“函数在区间(a,b)内处处存在有限导数”推广到“函数在区间(a,b)内只在有限个点处存在正(或负)无穷大的导数,其它点处均有有限导数”,证明了洛尔定理中的结论也成立.The extended application of the condition “limited region” of Rolle's theorem to “arbitrary region” proves that the conclusion of Rolle’s theorem is still tenable.And the extended application of the condition of Rolle’s theorem “a function has limited derivatives everywhere in the region(a,b)”to “a function has positive or negative infinite derivatives only at limited points in the region(a,b),and it has limited derivatives at other points”proves that the conclusion of Rolle's theorem is also tenable.

关 键 词：洛尔定理 连续 导数 正无穷导数 负无穷导数 

分 类 号：O172[理学—数学]