2012年全国硕士研究生入学考试英语试题National Entrance Test of English for MA/MS Candidates (NETEM) 跨考英语教研室—杨凤芝 Section Ⅰ Use of English Directions: Read the following text. Choose the best word(s) for each numbered blank and mark [A], [B], [C] or [D]on ANSWER SHEET 1. ( 10 points) The ethical judgments of the Supreme Court justices became an important issue recently. The court cannot_____ its legitimacy as guardian of the rule of law______ justices behave like politicians. Yet, in several instances, justices acted in ways that_____ the court’s reputation for being independent and impartial. Justices Antonin Scalia and Samuel Alito Jr., for example, appeared at political events. That kind of activity makes it less likely that the court’s decisions will be____ as im partial judgments. Part of the problem is that the justices are not _____ by an ethics code. At the very least, the court should make itself_______ to the code of conduct that ______to the rest of the federal judiciary. This and other cases ______the question of whether there is still a _____ between the court and politics. The framers of the Constitution envisioned law____ having authority apart from politics. They gave justices permanent positions ____ they would be free to ____those in power and have no need to_____ political support. Our legal system was designed to set law apart from politics precisely because they are so closely _____. Constitutional law is political because it results from choices rooted in fundamental social ______like liberty and property. When the court deals with social policy decisions, the law it _____is inescapably political — which is why decisions split along ideological lines are so easily _____ as unjust. The justices must _____doubts about the court’s legitimacy by maki ng themselves _____to the code of conduct. That would make their rulings more likely to be seen as separate from politics and, _____, convincing as law. 1 A emphasize B maintain C modify D recognize 2 A when B best C before D unless
2012年全国硕士研究生入学统一考试数学一试题 一、选择题:1:8小题，每小题4分，共32分.下列每题给出的四个选项中，只有一个选项符合题目要求的，请 将所选项前的字母填在答题纸．．． 指定位置上. (1) 曲线221 x x y x +=-渐近线的条数 ( ) (A) 0 (B) 1 (C) 2 (D) 3 (2) 设函数2()(1)(2)()x x nx y x e e e n =---L ,其中n 为正整数,则(0)y '= ( ) (A) 1(1)(1)!n n --- (B) (1)(1)!n n -- (C) 1(1)!n n -- (D) (1)!n n - (3) 如果函数(,)f x y 在(0,0)处连续,那么下列命题正确的是 ( ) (A) 若极限00(,)lim x y f x y x y →→+存在,则(,)f x y 在(0,0)处可微 (B) 若极限2200(,)lim x y f x y x y →→+存在,则(,)f x y 在(0,0)处可微 (C) 若(,)f x y 在(0,0)处可微,则 极限00(,)lim x y f x y x y →→+存在 (D) 若(,)f x y 在(0,0)处可微,则 极限2200 (,)lim x y f x y x y →→+存在 (4)设2 0sin (1,2,3)k x K e xdx k π==?I 则有 ( ) (A)123I I I << (B) 321I I I << (C) 231I I I << (D)213I I I << (5)设1100C α?? ?= ? ???,2201C α?? ?= ? ??? ,3311C α?? ?=- ? ??? ,4411C α-?? ?= ? ??? ,其中1234,,,C C C C 为任意常数，则下列向量组线性相关的 为( ) (A)123,,ααα (B) 124,,ααα (C)134,,ααα (D)234,,ααα (6) 设A 为3阶矩阵，P 为3阶可逆矩阵，且1100010002p AP -?? ?= ? ??? .若P=（123,,ααα），1223(,,)ααααα=+，则 1Q AQ -= ( )
2012年全国硕士研究生入学统一考试英语（二）试题 Section 1 Use of Eninglish Directions : Millions of Americans and foreigners see GI.Joe as a mindless war toy ,the symbol of American military adventurism, but that’s not how it used to be .To the men and women who 1 )in World War II and the people they liberated ,the GI.was the 2) man grown into hero ,the pool farm kid torn away from his home ,the guy who 3) all the burdens of battle ,who slept in cold foxholes,who went without the 4) of food and shelter ,who stuck it out and drove back the Nazi reign of murder .this was not a volunteer soldier ,not someone well paid ,5) an average guy ,up 6 )the best trained ,best equipped ,fiercest ,most brutal enemies seen in centuries。 His name is not much.GI. is just a military abbreviation 7) Government Issue ,and it was on all of the article 8) to soldiers .And Joe? A common name for a guy who never 9) it to the top .Joe Blow ,Joe Magrac …a working class name.The United States has 10) had a president or vicepresident or secretary of state Joe。 GI .joe had a career fighting German ,Japanese , and Korean troops . He appers as a character ,or a (12 ) of american personalities, in the 1945 movie The Story of GI. Joe, based on the last days of war correspondent Ernie Pyle. Some of the soldiers Pyleportrayde themselves in the film. Pyle was famous for covering the side of the warl, writing about the dirt-snow –and-mud soldiers, not how many miles wereor what towns were captured or liberated, His reportsthe “willie” cartoons of famed Stars and Stripes artist Bill Maulden. Both menthe dirt and exhaustion of war, the of civilization that the soldiers shared with each other and the civilians: coffee, tobacco, whiskey, shelter, sleep. Egypt, France, and a dozen more countries, G.I. Joe was any American soldier,the most important person in their lives。 1.[A] performed [B]served [C]rebelled [D]betrayed 2.[A] actual [B]common [C]special [D]normal 3.[A]bore [B]cased [C]removed [D]loaded 4.[A]necessities [B]facilitice [C]commodities [D]propertoes 5.[A]and [B]nor [C]but [D]hence 6.[A]for [B]into [C] form [D]against 7.[A]meaning [B]implying [C]symbolizing [D]claiming 8.[A]handed out [B]turn over [C]brought back [D]passed down 9.[A]pushed [B]got [C]made [D]managed 10.[A]ever [B]never [C]either [D]neither 11.[A]disguised [B]disturbed [C]disputed [D]distinguished 12.[A]company [B]collection [C]community [D]colony 13.[A]employed [B]appointed [C]interviewed [D]questioned 14.[A]ethical [B]military [C]political [D]human 15.[A]ruined [B]commuted [C]patrolled [D]gained 16.[A]paralleled [B]counteracted [C]duplicated [D]contradicted 17.[A]neglected [B]avoided [C]emphasized [D]admired 18.[A]stages [B]illusions [C]fragments [D]advancea 19.[A]With [B]To [C]Among [D]Beyond
2012年考研英语(二)真题试题及答案 Section 1 Use of Eninglish Directions : Millions of Americans and foreigners see GI.Joe as a mindless war toy ,the symbol of American military adventurism, but that’s not how it used to be .To the men and women who 1 )in World War II and the people they liberated ,the GI.was the 2) man grown into hero ,the pool farm kid torn away from his home ,the guy who 3) all the burdens of battle ,who slept in cold foxholes,who went without the 4) of food and shelter ,who stuck it out and drove back the Nazi reign of murder .this was not a volunteer soldier ,not someone well paid ,5) an average guy ,up 6 )the best trained ,best equipped ,fiercest ,most brutal enemies seen in centuries. His name is not much.GI. is just a military abbreviation 7) Government Issue ,and it was on all of the article 8) to soldiers .And Joe? A common name for a guy who never 9) it to the top .Joe Blow ,Joe Magrac …a working class name.The United States has 10) had a president or vicepresident or secretary of state Joe. GI .joe had a (11)career fighting German ,Japanese , and Korean troops . He appers as a character ,or a (12 ) of american personalities, in the 1945 movie The Story of GI. Joe, based on the last days of war correspondent Ernie Pyle. Some of the soldiers Pyle(13)portrayde themselves in the film. Pyle was famous for covering the (14)side of the warl, writing about the dirt-snow –and-mud soldiers, not how many miles were(15)or what towns were captured or liberated, His reports(16)the “willie” cartoons of famed Stars and Stripes artist Bill Maulden. Both men(17)the dirt and exhaustion of war, the (18)of civilization that the soldiers shared with each other and the civilians: coffee, tobacco, whiskey, shelter, sleep. (19)Egypt, France, and a dozen more countries, G.I. Joe was any American soldier,(20)the most important person in their lives. 1.[A] performed [B]served [C]rebelled [D]betrayed 2.[A] actual [B]common [C]special [D]normal 3.[A]bore [B]cased [C]removed [D]loaded 4.[A]necessities [B]facilitice [C]commodities [D]propertoes 5.[A]and [B]nor [C]but [D]hence 6.[A]for [B]into [C] form [D]against 7.[A]meaning [B]implying [C]symbolizing [D]claiming 8.[A]handed out [B]turn over [C]brought back [D]passed down 9.[A]pushed [B]got [C]made [D]managed 10.[A]ever [B]never [C]either [D]neither 11.[A]disguised [B]disturbed [C]disputed [D]distinguished 12.[A]company [B]collection [C]community [D]colony 13.[A]employed [B]appointed [C]interviewed [D]questioned 14.[A]ethical [B]military [C]political [D]human 15.[A]ruined [B]commuted [C]patrolled [D]gained 16.[A]paralleled [B]counteracted [C]duplicated [D]contradicted
高等数学部分易混淆概念 第一章：函数与极限 一、数列极限大小的判断 例1：判断命题是否正确． 若()n n x y n N <>，且序列,n n x y 的极限存在，lim ,lim ,n n n n x A y B A B →∞ →∞ ==<则 解答：不正确．在题设下只能保证A B ≤， 不能保证A B <．例如：11 ,1 n n x y n n ==+，,n n x y n ，那么函数()f x 在X 上无界． 无穷大：设函数 ()f x 在0x 的某一去心邻域内有定义（或x 大于某一正数时有定义） ．如果对于任意给定的正数M （不论它多么大），总存在正数δ（或正数 X ） ，只要x 适合不等式00x x δ<-<（或 x X >），对应的函数值()f x 总满足不等式
2012年全国硕士研究生入学统一考试英语试题 Section Ⅰ Use of English Directions: Read the following text. Choose the best word(s) for each numbered blank and mark A, B, C or D on ANSWER SHEET 1. (10 points) The ethical judgments of the Supreme Court justices have become an important issue recently. The court cannot 1 its legitimacy as guardian of the rule of law 2 justices behave like politicians. Yet, in several instances, justices acted in ways that 3 the court’s reputation for being independent and impartial. Justice Antonin Scalia, for example, appeared at political events. That kind of activity makes it less likely that the court’s decisions will be 4 as impartial judgments. Part of the problem is that the justices are not 5 by an ethics code. At the very least, the court should make itself 6 to the code of conduct that 7 to the rest of the federal judiciary. This and other similar cases 8 the question of whether there is still a 9 between the court and politics. The framers of the Constitution envisioned law 10 having authority apart from politics. They gave justices permanent positions 11 they would be free to 12 those in power and have no need to 13 political support. Our legal system was designed to set law apart from politics precisely because they are so closely 14 . Constitutional law is political because it results from choices rooted in fundamental social 15 like liberty and property. When the court deals with social policy decisions, the law it 16 is inescapably political—which is why decisions split along ideological lines are so easily 17 as unjust. The justices must 18 doubts about the court’s legitimacy by making themselves 19 to the code of conduct. That would make ruling more likely to be seen as separate from politics and, 20 , convincing as law. 1. [A] emphasize [B] maintain [C] modify [D] recognize 2. [A] when [B] lest [C] before [D] unless 3. [A] restored [B] weakened [C] established [D] eliminated 4. [A] challenged [B] compromised [C] suspected [D] accepted 5. [A] advanced [B] caught [C] bound [D] founded 6. [A] resistant [B] subject [C] immune [D] prone 7. [A] resorts [B] sticks [C] loads [D] applies 8. [A] evade [B] raise [C] deny [D] settle 9. [A] line [B] barrier [C] similarity [D] conflict 10. [A] by [B] as [C] though [D] towards 11. [A] so [B] since [C] provided [D] though 12. [A] serve [B] satisfy [C] upset [D] replace 13. [A] confirm [B] express [C] cultivate [D] offer 14. [A] guarded [B] followed [C] studied [D] tied 15. [A] concepts [B] theories [C] divisions [D] conceptions 16. [A] excludes [B] questions [C] shapes [D] controls
２0１2年考研数学三真题 一、选择题(１~8小题，每小题４分,共３2分。下列每题给出的四 个选项中,只有一个选项是符合题目要求的。） (1)曲线y=x 2+x x2?1 渐近线的条数为 (Ａ)0 (B）1 (C)2 （D)3 【答案】C。 【解析】 由lim x→+∞y=lim x→+∞ x2+x x2?1 =1=lim x→?∞ y=lim x→?∞ x2+x x2?1 ， 得y=1是曲线的一条水平渐近线且曲线没有斜渐近线； 由lim x→1y=lim x→1 x2+x x?1 =∞得x=1是曲线的一条垂直渐近线； 由lim x→?1y=lim x→?1 x2+x x?1 =1 2 得x=?1不是曲线的渐近线; 综上所述，本题正确答案是C 【考点】高等数学—一元函数微分学—函数图形的凹凸、拐点及渐近线 (2)设函数f(x)=(e x?1)(e2x?2)?(e nx?n)，其中n为正整数， 则f′(0)= （A）(?1)n?1(n?1)! (B)(?1)n(n?1)! （C)(?1)n?1(n)! (D）(?1)n(n)! 【答案】A 【解析】 【方法1】
令g (x )=(e 2x ?2)?(e nx ?n)，则 f (x )=(e x ?1) g (x ) f ′(x)=e x g (x )+(e x ?1)g′(x ) f ′(0)= g (0)=(?1)(?2)?(?(n ?1)) =(?1)n?1(n ?1)! 故应选Ａ． 【方法2】 由于f (0)=0,由导数定义知 f ′(0)=lim x→0f(x)x =lim x→0 (e x ?1)(e 2x ?2)?(e nx ?n)x =lim x→0(e x ?1)x ?lim x→0(e 2x ?2)?(e nx ?n) =(?1)(?2)?(?(n ?1))=(?1)n?1(n ?1)!. 【方法3】 排除法，令n =2,则 f (x )=(e x ?1)(e 2x ?2) f ′(x )=e x (e 2x ?2)+2e 2x (e x ?1) f ′(0)=1?2=?1 则（B)(C)（D)均不正确 综上所述，本题正确答案是(A ） 【考点】高等数学—一元函数微分学—导数和微分的概念 (3)设函数f(t)连续，则二次积分∫dθπ20∫f(r 2)rdr 22cos θ = (A )∫dx 20∫√x 2+y 2f(x 2+y 2)dy √4?x 2√2x?x 2 (Ｂ) ∫dx 20 ∫f(x 2+y 2)dy √4?x 2√2x?x 2
2020考研数学复习指导 教材是同济五版线性代数，1-5章：行列式、矩阵及其运算、矩阵的初等变换及其方程组、向量组的线性相关性、相似矩阵及二次型。数三不考向量组的线性相关性中的向量空间，线性方程组跟空间解析几何结合的问题; 概率与数理统计的内容包括：1、概率论的基本概念2、随机变量及其分布3、多维随机变量及其分布4、随机变量的数字特征5、大数定律及中心极限定理6、样本及抽样分布7、参数估计，其中数三的同学不考参数估计中的区间估计。 3.对应考试的专业 数学一是报考理工科的学生考，考试内容包括高等数学，线性代数和概率论与数理统计，考试的内容是最多的。 数学二是报考农学的学生考，考试内容只有高等数学和线性代数，但是高等数学中删去的较多，是考试内容最少的 数学三是报考经济学的学生考，考试内容是高等数学，线性代数和概率统计。高数部分中，主要重视微积分的考察，概率统计中没有假设检验和置信区间。 4.难度上的区别 数学一最大，数学三最小。数学一的难度主要体现在内容多，给考生的复习加大了难度;而数学二由于内容较少，试题的灵活性也
相对较大。但总的来说，数一数二和数三区别不大，在都考的部分，要求是差不多的，考试中三张试卷中完全相同的试题也占到了很大比重。 二、数学该如何复习 1.首先就要明确高频的考题 高频的考题其实就是命题的重点，一般的情况下，这样的命题是要年年进行考查的。 ?微积分 (1)幂指函数这样的未定式的极限，是重点考查的内容。 (2)利用定积分的定义，像中值定理来进行极限的计算，这样的内容虽然它未必是高频的考题，但也要重视。 (3)一元函数的微分学，求导运算它是微积分的基础，也是考查的重点内容。在函数的求导问题当中，数一、数二由参数方程所确定的函数的导数，分段函数的可导性，都是高频的考题。 (4)幂指函数的求导、复合函数的求导，它也会偶尔进行考查。 (5)一元函数微分学的应用，每年是必考的内容，研究函数的性态，函数单调性、极值、最值和凹凸性，极值和最值的问题，就是绝对高频的考点，几乎年年都要进行考查。 (6)对于凹凸性这样的问题，也不能忽视。比如说利用单调性、凹凸性、极值和最值来证明不等式，要掌握这类问题的常规的解题模式和方法。 (7)一元函数积分学，高频内容就是积分上限函数。要重点掌握
Section I Use of English Directions: Read the following text. Choose the best word(s) for each numbered blank and mark A, B, C or D on ANSWER SHEET 1. (10 points) Read the following text. Choose the best word(s) for each numbered blank and mark A, B, C or D on ANSWER SHEET 1. (10 points) The ethical judgments of the Supreme Court justices have become an important issue recently. The court cannot _1_ its legitimacy as guardian of the rule of law _2_ justices behave like politicians. Yet, in several instances, justices acted in ways that _3_ the court’s reputation for being independent and impartial. Justice Antonin Scalia, for example, appeared at political events. That kind of activity makes it less likely that the court’s decisions will be _4_ as impartial judgments. Part of the problem is that the justices are not _5_by an ethics code. At the very least, the court should make itself _6_to the code of conduct that _7_to the rest of the federal judiciary. This and other similar cases _8_the question of whether there is still a _9_between the court and politics. The framers of the Constitution envisioned law _10_having authority apart from politics. They gave justices permanent positions _11_they would be free to _12_ those in power and have no need to _13_ political support. Our legal system was designed to set law apart from politics precisely because they are so closely _14_.
2012年全国硕士研究生入学统一考试英语(二)试题答案详解Section I Use of English 1.【答案】B 【解析】从空后的句子“他们解放的人们”可以看出，空前的句子表示的应该是参加了第二次大战的男人和女人。只有serve有“服兵役”的意思，所以选B。其他都不符合题意。 2.【答案】B 【解析】空内信息应该是与hero“英雄”意思相对，后面的分句说他背井离乡，经历了很多苦难，显然这里应该是说由普通人平凡人(common man)成长为英雄，所以选B。 3.【答案】A 【解析】本题考查的是词语的搭配关系，承担战争带来的负担，应该用动词bear或shoulder，所以这里选A，bore。 4.【答案】A 【解析】necessities表示“生活必需品”，空外信息food和shelter(食物和住宿)这些就是维持生存最起码的条件。Facilities是设备设施，commodities商品，properties财产，均不符合题意。 5.【答案】C 【解析】not…but，“不是，而是”表转折，不是自愿兵，也没有高的报酬，而是一个普通人。所以选C。 6.【答案】D 【解析】这道题主要考查介词的搭配。根据up______(the best trained, bestequipped, fiercest, most brutal).enemies可以知道是起来反抗敌人，所以选D选项against。 7.【答案】C 【解析】GI。在军事上是Government Issue 的缩略语，所以，GL。这个符号就是象征着这个全称Government Issue。选C。 8.【答案】A 【解析】该句意思为，GI。这个符号出现在给士兵分发的所有物品上，hand out “分发，发放”符合题意。Turn over “移交”，bring back“带回”，pass down“传承，一代一代传下来”在句意上都说不通。 9.【答案】C 【解析】空所在句子的语境为：Joe是个普通名词，一个从未爬到社会顶层的人的名字。Manage表示再怎么经过努力，最终也未获得成功，所以选C。 10.【答案】B 【解析】结合第9题的分析可知，空所在句子实际上是进一步举例说明Joe没有取得大的成就：从来都不曾出现叫做Joe的总统、副总统、国务卿。根据句意只能选never，B。 11.【答案】D 【解析】本题考察词汇辨析。空所在的语境为：GI .Joe有_ _ 的军旅生涯，曾和德国，美国以及韩国的军队作战。由此语境确定选D，其他几项均不符合题意。 12.【答案】B 【解析】本题考察词汇辨析。空所在语境为：他身上体现着美国人的某些特色，或身上结合了美国人的诸多特性。结合语境，可知作者想表达在他身上有很多美国人的典型特色，因而选B。 13.【答案】C 【解析】本题考察词汇辨析。空所在语境为：Pyle _ _ 的士兵也本色出演了该片。结合上句对Ernie Pyle的介绍，可知为一战地记者(warcorrespondent)，确定答案C。
2012考研数学一大纲 考试科目：高等数学、线性代数、概率论与数理统计 考试形式和试卷结构 一、试卷满分及考试时间 试卷满分为150分，考试时间为180分钟. 二、答题方式 答题方式为闭卷、笔试. 三、试卷内容结构 高等教学 56% 线性代数 22% 概率论与数理统计 22% 四、试卷题型结构 单选题 8小题，每题4分，共32分 填空题 6小题，每题4分，共24分 解答题(包括证明题) 9小题，共94分 高 等 数 学 一、函数、极限、连续 考试内容 函数的概念及表示法 函数的有界性、单调性、周期性和奇偶性 复合函数、反函数、分段函数和隐函数 基本初等函数的性质及其图形 初等函数 函数关系的建立 数列极限与函数极限的定义及其性质 函数的左极限与右极限 无穷小量和无穷大量的概念及其关系 无穷小量的性质及无穷小量的比较 极限的四则运算 极限存在的两个准则：单调有界准则和夹逼准则 两个重要极限: 函数连续的概念 函数间断点的类型 初等函数的连续性 闭区间上连续函数的性质 考试要求 1.理解函数的概念，掌握函数的表示法，会建立应用问题的函数关系. 2.了解函数的有界性、单调性、周期性和奇偶性. 3.理解复合函数及分段函数的概念，了解反函数及隐函数的概念. 4.掌握基本初等函数的性质及其图形，了解初等函数的概念. 5.理解极限的概念，理解函数左极限与右极限的概念以及函数极限存在与左、右极限之间的关系. 6.掌握极限的性质及四则运算法则. 7.掌握极限存在的两个准则，并会利用它们求极限，掌握利用两个重要极限求极限的方法. 8.理解无穷小量、无穷大量的概念，掌握无穷小量的比较方法，会用等价无穷小量求极限. 9.理解函数连续性的概念(含左连续与右连续)，会判别函数间断点的类型. 10.了解连续函数的性质和初等函数的连续性，理解闭区间上连续函数的性质(有界性、最大值和最小值定理、介值定理)，并会应用这些性质. 二、一元函数微分学 考试内容 导数和微分的概念 导数的几何意义和物理意义 函数的可导性与连续性之间的关系 平面曲线的切线和法线 导数和微分的四则运算 基本初等函数的导数 复合函数、反函数、隐函数以及参数方程所确定的函数的微分法 高阶导数 一阶微分形式的不变性 微分中值定理 洛必达(L’Hospi tal)法则 函数单调性的判别 函数的极值 函数图形的凹凸性、拐点及渐近线 函数图形的描绘 函数的最大值和最小值 弧微分 曲率的概念 曲率圆与曲率半径 考试要求 1.理解导数和微分的概念，理解导数与微分的关系，理解导数的几何意义，会求平面曲线的切线方程和法线方程，了解导数的物理意义，会用导数描述一些物理量，理解函数的可导性与连续性之间的关系. 2.掌握导数的四则运算法则和复合函数的求导法则，掌握基本初等函数的导数公式.了解微分的四则运算法则和一阶微分形式的不变性，会求函数的微分. 0sin 1lim 1lim 1x x x x e x x →→∞??=+= ???
第三章 中值定理与导数的应用 ?????? ? ? ?? ?? ?? ??????????? ?????????????? ??必要条件求解函数的性态，充分渐近线凹凸性，拐点单调性，极值，最值—求极限—洛必达法则—应用数，求极限证明，确定无穷小的阶泰勒中值定理柯西中值定理拉格朗日中值定理罗尔定理中值定理 第一节 微分中值定理
极值:设) f在0x的某一邻域) (x U内有定义，若 (0x 对一切) ) ( (0x f≤,则 f≥)) x f ( U (0x x ( x∈有) f (0x ) 称) (x f的极f在0x取得极小（大）值，称0x是) (x 小（大）值点，极小值和极大值统称为极值，极小值点和极大值点统称为极值点。 费马引理：设) f在0x (x f'存在， (0x x=取极值，又)
则0)(0='x f 。 在0x x =取极值的必要条件：可导的极值点导数必为零。
驻点：若0)(='a f ，则称a x =为)(x f 的驻点。 可导的极值点一定为驻点，但是驻点不一定为极值点。 定理1（罗尔定理）： 条件： ①)(x f 在],[b a 上连续； ②在),(b a 可导； ③)()(b f a f = 结论： 一定存在),(b a ∈ξ，
使得0)(='ξf 。 几何意义：设AB 是 （1）定义在],[b a 上的光滑曲线)(x f y =； （2）若除端点外处处有不垂直于x 轴的切线； （3）两端点纵坐标相等 则在AB 上至少存在一点C ，其切线是水平的． 即两端点同高的连续曲线内至少有一点的切线是水平的．（如图所示）