2017年考研英语一真题原文及答案解析完整版 2017年全国硕士研究生入学统一考试英语（一） 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 the ANSWER SHEET. (10 points) Could a hug a day keep the doctor away? The answer may be a resounding “yes!” 1 helping you feel close and 2 to people you care about, it turns out that hugs can bring a 3 of health benefits to your body and mind. Believe it or not, a warm embrace might even help you 4 getting sick this winter. In a recent study 5 over 400 health adults, researchers from Carnegie Mellon University in Pennsylvania examined the effects of perceived social support and the receipt of hugs 6 the participants’ susceptibility to developing the common cold after being 7 to the virus .People who perceived greater social support were less likely to come 8 with a cold ,and the researchers 9 that the stress-reducing effects of hugging 10 about 32 percent of that beneficial effect. 11 among those who got a cold, the ones who felt greater social support and received more frequent hugs had less severe 12 . “Hugging protects people who are under stress from the 13 risk for colds that’s usually 14 with stress,” notes Sheld on Cohen, a professor of psychology at Carnegie. Hugging “is a
2017年全国硕士研究生入学统一考试数学(一)试卷 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 ）若函数0(),0x f x b x >=?≤? 在0x =处连续，则（ ） (A)12ab = (B)12ab =- (C)0ab = (D)2ab = （2）设函数()f x 可导，且()()0f x f x '>则（ ） (A)()()11f f >- (B) ()()11f f <- (C)()()11f f >- (D)()()11f f <- （3）函数()22,,f x y z x y z =+在点()1,2,0处沿向量()1,2,2n 的方向导数为（ ） (A)12 (B)6 (C)4 (D)2 （4）甲乙两人赛跑，计时开始时，甲在乙前方10（单位:m ）处,如下图中，实线表示甲的速度曲线()1v v t = （单位:m/s ）虚线表示乙的速度曲线()2v v t =，三块阴影部分面积的数值依次为10，20，3，计时开始后乙追上甲的时刻记为0t （单位:s ）,则（ ） (A)010t = (B)01520t << (C)025t = (D)025t > ()s （5）设α为n 维单位列向量，E 为n 阶单位矩阵，则（ ） (A) T E αα-不可逆 (B) T E αα+不可逆 (C) 2T E αα+不可逆 (D)2T E αα-不可逆 （6）已知矩阵200021001A ????=?????? 2100200 01B ????=??????100020002C ????=??????，则（ ） (A) A 与C 相似，B 与C 相似 (B) A 与C 相似，B 与C 不相似 (C) A 与C 不相似，B 与C 相似 (D) A 与C 不相似，B 与C 不相似
2020年研究生入学统一考试试题（英语一） 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 the ANSWER SHEET. (10 points) Even if families are less likely to sit down to eat together than was once the case, millions of Britons will none the less have partaken this weekend of one of the nation's great traditions: the Sunday roast. __1__ a cold winter's day, few culinary pleasures can __2__it. Yet as we report now, the food police are determined that this __3__ should be rendered yet another guilty pleasure __4__ to damage our health. The Food Standards Authority (FSA) has __5__ a public warning about the risks of a compound called acrylamide that forms in some foods cooked __6__ high temperatures.This means that people should __7__ crisping their roast potatoes, spurn thin-crust pizzas and only __8__ toast their bread. But where is the evidence to support such alarmist advice? __9__ studies have shown that acrylamide can cause neurological damage in mice, there is no __10__ evidence that it causes cancer in humans. Scientists say the compound is "__11__ to be carcinogenic" but have no hard scientific proof. __12__ the precautionary principle, it could be argued that it is __13__ to follow the FSA advice. __14__, it was rumored that smoking caused cancer for years before the evidence was found to prove a __15__. Doubtless a piece of boiled beef can always be __16__ up on Sunday alongside some steamed vegetables,without the Yorkshire pudding and no wine. But would life be worth living? __17__, the FSA says it is not telling people to cut out roast foods __18__, but to reduce their lifetime intake. However, their __19__ risks coming across as exhortation and nannying. Constant health scares just __20__ with no one listening. 1. A In B Towards C On D Till 2. A match B express C satisfy D influence 3. A patience B enjoyment C surprise D concern 4. A intensified B privileged C compelled D guaranteed 5. A issued B received C ignored D canceled 6. A under B at C for D by 7. A forget B regret C finish D avoid 8. A partially B regularly C easily D initially 9. A Unless B Since C If D While 10. A secondary B external C inconclusive D negative 11. A insufficient B bound C likely D slow 12. A On the basis of B At the cost of C In addition to D In contrast to 13. A interesting B advisable C urgent D fortunate 14. A As usual B In particular C By definition D After all 15. A resemblance B combination C connection D pattern 16. A made B served C saved D used 17. A To be fair B For instance C To be brief D in general 18. A reluctantly B entirely C gradually D carefully 19. A promise B experience C campaign D competition 20. A follow up B pick up C open up D end up 解析：
2017年全国硕士研究生入学统一考试数学二试题解析 一、选择题：1～8小题，每小题4分，共32分，下列每小题给出的四个选项中，只有一项符合题目要求的，请将所选项前的字母填在答题纸．．． 指定位置上. （1） ）若函数0(),0x f x b x >=?≤? 在0x =处连续，则（ ） (A)12 ab = (B)12 ab =- (C)0ab = (D)2ab = 【答案】A 【解析】00112lim lim ,()2x x x f x ax a ++→→==Q 在0x =处连续11.22b ab a ∴=?=选A. （2）设二阶可导函数()f x 满足(1)(1)1,(0)1f f f =-==-且'' ()0f x >，则（ ） ()()1 1 110 1 1 1 10()()0 ()0()()()()()A f x dx B f x dx C f x dx f x dx D f x dx f x dx ----><>
2017年考研数学一真题 一、选择题 1—8小题．每小题4分，共32分． １．若函数0(),0x f x b x >=?≤? 在0x =处连续，则 （A ）12ab = （B ）1 2 ab =-（C ）0ab =（D ）2ab = 【详解 】0001112lim ()lim lim 2x x x x f x ax ax a +++→→→-===，0lim ()(0)x f x b f -→==，要使函数在0x =处连续，必须满足11 22 b ab a =?=．所以应该选（A ） 2．设函数()f x 是可导函数，且满足()()0f x f x '>，则 （A ）(1)(1)f f >- （B ）11()()f f <- （C ）11()()f f >- （D ）11()()f f <- 【详解】设2()(())g x f x =，则()2()()0g x f x f x ''=>，也就是()2 ()f x 是单调增加函数．也就得到 () ()2 2 (1)(1)(1)(1)f f f f >-?>-，所以应该选（C ） 3．函数22(,,)f x y z x y z =+在点(1,2,0)处沿向量(1,2,2)n =的方向导数为 （A ）12 （B ）6 (C ）4 （D ）2 【详解】 22,,2f f f xy x z x y z ???===???，所以函数在点(1,2,0)处的梯度为()4,1,0gradf =，所以 22(,,)f x y z x y z =+在点(1,2,0)处沿向量(1,2,2)n =的方向导数为 ()01 4,1,0(1,2,2)23f gradf n n ?=?=?=?应该选（D ） ４．甲、乙两人赛跑，计时开始时，甲在乙前方10（单位：米）处，如图中，实线表示甲的速度曲线1()v v t =（单位：米/秒），虚线表示乙的速度曲线2()v v t =（单位：米/秒），三块阴影部分的面积分别为10,20,3，计时开始后乙追上甲的时刻为0t ，则（ ） （A ）010t = （B ）01520t << （C ）025t = （D ）025t > 【详解】由定积分的物理意义：当曲线表示变速直线
2017年考研英语一真题-高清版含答案 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 the ANSWER SHEET.(10points) Could a hug a day keep the doctor away?The answer may be a resounding “yes!”1helping you feel close and2to people you care about,it turns out that hugs can bring a3of health benefits to your body and mind. Believe it or not,a warm embrace might even help you4getting sick this winter. In a recent study5over400healthy adults,researchers from Carnegie Mellon University in Pennsylvania examined the effects of perceived social support and the receipt of hugs6the participants’susceptibility to developing the common cold after being7to the virus.People who perceived greater social support were less likely to come8with a cold,and the researchers9that the stress-reducing effects of hugging10about 32percent of that beneficial effect.11among those who got a cold,the ones who felt greater social support and received more frequent hugs had less severe 12. “Hugging protects people who are under stress from the13risk for colds that’s usually14with stress,”notes Sheldon Cohen,a professor of psychology at Carnegie.Hugging“is a marker of intimacy and helps15the feeling that others are there to help16difficulty.” Some experts17the stress-reducing,health-related benefits of hugging to the release of oxytocin,often called“the bonding hormone”18it promotes attachment in relationships,including that between mothers and their newborn babies.Oxytocin is made primarily in the central lower part of the brain, and some of it is released into the bloodstream.But some of it19in the brain,where it20mood,behavior and physiology.
2017年考研数学三真题及解析 一、选择题 1—8小题．每小题4分，共32分． 1 ．若函数0(),0x f x b x >=?≤? 在0x =处连续，则 （A ）12ab = （B ）1 2 ab =-（C ）0ab =（D ）2ab = 【详解】0001112lim ()lim lim 2x x x x f x ax ax a +++→→→-=== ，0lim ()(0)x f x b f -→==，要使函数在0x =处连续，必须满足11 22 b ab a =?=．所以应该选（A ） 2．二元函数(3)z xy x y =--的极值点是（ ） （A ）(0,0) （B ）03(,) （C ）30(,) （D ）11(,) 【详解】 2(3)32z y x y xy y xy y x ?=---=--?，232z x x xy y ?=--?， 解方程组2 2320320z y xy y x z x x xy y ??=--=??????=--=???，得四个驻点．对每个驻点验证2 AC B -，发现只有在点11(,)处满足 230AC B -=>，且20A C ==-<，所以11(,)为函数的极大值点，所以应该选（D ） 3．设函数()f x 是可导函数，且满足()()0f x f x '>，则 （A ） (1)(1)f f >- （B ）11()()f f <- （C ）11()()f f >- （D ）11()()f f <- 【详解】设2 ()(())g x f x =，则()2()()0g x f x f x ''=>，也就是()2 ()f x 是单调增加函数．也就得到 () ()2 2 (1)(1)(1)(1)f f f f >-?>-，所以应该选（C ） 4． 若级数 21 1sin ln(1)n k n n ∞ =??--??? ?∑收敛，则k =（ ） （A ）1 （B ）2 （C ）1- （D ）2- 【详解】iv n →∞时22221111111111sin ln(1)(1)22k k k o k o n n n n n n n n n ???????? --=---+=++ ? ? ? ? ????? ???? 显然当且仅当(1)0k +=，也就是1k =-时， 级数的一般项是关于1 n 的二阶无穷小，级数收敛，从而选择（C ）．
武汉大学2017年自主招生 武汉大学进行了2017年自主招生以面试为主，部分专业有笔试。主要是考核学生在报考专业领域展现出的学科能力和创新思维潜质。文学院面试不设考题，3位考官向学生随机发问。考生拿到题后有几分钟思考时间，然后面对3位考官进行陈述。考官可能对考生的某个观点提出疑问。 部分笔试真题 武大历史专业笔试题目选材于历史理论著作《文史通义》。考生需根据文字进行断句，并作出解析，写明自己的观点。 考生表示理科笔试题难于高考题，但易于奥赛题，生物部分专业知识多为大学内容。 生物：涉及植物生活史、超级细菌、植物传粉等 物理：光、声、磁场等知识 数学：5道简答题，分别考察概率、向量及三角函数、解析几何、数列求和、多项式系数等知识点。 历史：选材于历史理论著作《文史通义》。根据文字进行断句，并作出解析，写明自己的观点。考题以繁体字形式呈现。 数学与统计学院笔试共有5道简答题，分别考察概率、向量及三角函数、解析几何、求和、多项式系数等方面的知识点。 部分面试真题
1、“怼”这个字近来在网络上流行，你是如何看待这个生僻字在网上流行的？（马克思学院） 2、文化遗民是入乡随俗还是文化独立（哲学院） 3、人工智能对社会发展的影响（马克思主义哲学） 4、西江月、永遇乐、卜算子等几个词牌名中，哪一个对应的字数最多？（国学院） 5、古代平民为什么没有姓和氏？ 6、成吉思汗为什么要西征？（文学院） 7、令你印象最深刻的一节语文课是什么？（文学院） 8、解释"喜大普奔" 9、何为"电脑寡妇" 10、解释"人艰不拆"等网络热词 11、对人工智能创作文学作品的看法 12、你看过《欢乐颂》吗？谈谈你对曲筱绡和关雎尔的看法（马克思主义学院） 13、你当班长多年，能分别谈一谈如何解决男男同学之间的矛盾、男女同学之间的矛盾以及女女同学之间的矛盾吗？（马克思主义学院） 14、有人说没有真实的历史，历史都是杜撰出来的，你怎么看？（历史与文化学院） 15、你喜欢生活在哪个朝代，为什么？（历史与文化学院）
2017考研真题答案：2017考研英语一真题试卷及答案（完整版）2017年全国硕士研究生入学统一考试英语(一)试题+【答案】 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 the ANSWER SHEET. (10 points) Could a hug a day keep the doctor away? The answer may be health benefits to your body and mind. Believe it or not, a warm from Carnegie Mellon University in Pennsylvania examined the the participants' susceptibility to developing the common cold
who got a cold, the ones who felt greater social support and Cohen, a professor of psychology at Carnegie. Hugging "is a benefits of hugging to the release of oxytocin, often called "the relationships, including that between mother and their newborn babies. Oxytocin is made primarily in the central lower part of the brain , and some of it is released into the bloodstream. But physiology. 1.[A] Unlike [B] Besides [C] Despite [D] Throughout 【答案】[B] Besides 2.[A] connected [B] restricted [C] equal [D] inferior 【答案】[A] connected
2017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，只有一个选项是符合题目要求的．请将所选项前的字母填在答题纸．．． 指定位置上． （1 ）若函数0(),0x f x b x >=?≤? 在x 连续，则 (A) 12 ab =． (B) 12 ab =- ． (C) 0ab =． (D) 2ab =． 【答案】A 【详解】由0 1 lim 2x b a + →==,得12ab =. （2）设函数()f x 可导，且()'()0f x f x >则 (A) ()()11f f >- ． (B) ()()11f f <-． (C) ()()11f f >-． (D) ()()11f f <-. 【答案】C 【详解】2() ()()[]02 f x f x f x ''=>,从而2()f x 单调递增,22(1)(1)f f >-. （3）函数2 2 (,,)f x y z x y z =+在点(1,2,0)处沿着向量(1,2,2)n =的方向导数为 (A) 12． (B) 6． (C) 4． (D)2 ． 【答案】D 【详解】方向余弦12cos ,cos cos 33 = ==αβγ,偏导数22,,2x y z f xy f x f z '''===,代入cos cos cos x y z f f f '''++αβγ即可. （4）甲乙两人赛跑，计时开始时，甲在乙前方10(单位：m)处.图中，实线表示甲的速度曲线1()v v t =(单位：m/s)，虚线表示乙的速度曲线2()v v t =(单位：m/s)，三块阴影部分面积的数值一次为10，20，3，计时开始后乙追上甲的时刻记为(单位：s)，则
析2017年考研英语考试已经结束!出国留学考研网在考后第一时间为大家提供2017年考研英语一翻译真题及答案解析，更多考研资讯请关注我们网站的更新! 2017年考研英语一翻译真题及答案解析 英语1文章明显偏学术，今年考察英语语言发展情况，文章选的英国文化教育协会，是雅思出题组织者。它的主席叫大卫格兰多的一本书，叫《英语下一步》，他讲到整本书意思是英语将走向何处。 很有意思的是主席曾经这本书里说到了中文将以后成为世界语言。 英语1考题作为序言部分作为考题。 今年英语1总体难度和去年相比，刚刚过去2016年考研题稳中有一点点上升，没有任何难句出现，只是长句。我认为稳中上升。 第一句话有一个单词难一点，(英文)，英语全球性主导地位。翻译里没有考过。(英文)主导地位考过，但是是阅读里经常出现，翻译都是可以的。这句话基本意思说到了，说英语的人进一步扩大，这是一个(英文)状语从句。后面跟着有迹象表明，是主句，表明的迹象是什么呢?从句，英语全球性主导地位在可预见地位将减弱。 fade(英文)略微有难度。我对考研阅读没有那么熟，但是2000年出现过。 如果按照新东方老师关注的精读方法来学习有很好的效果。 第二句话讲到了大卫这个人分析，会终结一些人的(英文)，他们或许会认为英语全球性地位是如此稳定。他们有一次词，是(英语)如此稳定，英国年轻一代不需要额外学习其他的语言能力。但是会终结年轻一代的能力。 但是组织的时候要注意一下，有些人认为英语语言地位如此稳定，英国年轻人没有必要学习什么，但是大卫的观点会终结这些人的想法。语序颠倒一下会更好。48题，正在引入英语，引入小学课程，有一个单词，(英语)，这个单
2017年考研英语一（答案及解析） Section I Use of English Directions: Read the following text. Choose the best word(s) from each numbered blank and mark A, B, C or D on the ANSWER SHEET.(10 points) Could a hug a day keep the doctor away? The answer may be a resounding "yes!" ___1__ helping you feel close and __2___to people you care about, it turns out that hugs can bring a ___3__ of health benefits to your body and mind. Believe it or not, a warm embrace might even help you __4___ getting sick this winter. In a recent study ___5__ over 400 healthy adults,researchers from Carnegie Mellon University in pennsylvania examined the effects of perceived social support and the receipt of hugs ___6__ the participants' susceptibility to developing the common cold after being ___7__ to the virus. People who perceived greater social support were less likely to come ___8__ with a cold, and the researchers __9___ that the stress-reducing effects of hugging ___10__ about 32 percent of that beneficial effect. ___11__ among those who got a cold, the ones who felt greater social support and received more frequent hugs had less severe __12___. "Hugging protects people who are under stress from the ___13__ risk for colds that's usually __14___ with stress," Notes sheldon Cohen, a professor of psychology at Carnegie. Hugging "is a marker of intimacy and helps __15___ the feeling that others are there to help ___16__difficulty." Some experts ___17__ the stress-reducing,health-related benefits of hugging to the release of oxytocin, often called"the bonding hormone" __18___ it promotes attachment in relationships, including that between mothers and their newborn babies. Oxytocin is made primarily in the central lower part of the brain, and some of it is released into the bloodstream. But some of it___19__ in the brain, where it __20___ mood, behavior and physiology. 1. [A]Besides[B]Unlike[C]Throughout[D]Despite 2. [A]equal[B]restricted[C]connected[D]inferior
2016考研数学三真题及答案 一、填空题：1－6小题，每小题4分，共24分. 把答案填在题中横线上. （1）()11lim ______.n n n n -→∞ +?? = ??? （2）设函数()f x 在2x =的某邻域内可导,且()() e f x f x '=，()21f =，则()2____.f '''= （3）设函数()f u 可微,且()1 02 f '= ,则()224z f x y =-在点(1,2)处的全微分() 1,2d _____.z = （4）设矩阵2112A ?? = ?-?? ，E 为2阶单位矩阵，矩阵B 满足2BA B E =+，则=B . （5）设随机变量X Y 与相互独立，且均服从区间[]0,3上的均匀分布，则 {}{}max ,1P X Y ≤=_______. （6）设总体X 的概率密度为()()121,,,,2 x n f x e x X X X -= -∞<<+∞为总体X 的简 单随机样本，其样本方差为2 S ，则2 ____.ES = 二、选择题：7－14小题，每小题4分，共32分. 每小题给出的四个选项中，只有一项符合题目要求，把所选项前的字母填在题后的括号内. （7）设函数()y f x =具有二阶导数，且()0,()0f x f x '''>>，x ?为自变量x 在点0x 处的增量，d y y ?与分别为()f x 在点0x 处对应的增量与微分，若0x ?>，则 (A) 0d y y <
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 the ANSWER SHEET. (10 points) Could a hug a day keep the doctor away? The answer may be a resounding “yes!” 1 helping you feel close and 2 to people you care about, it turns out that hugs can bring a 3 of health benefits to your body and mind. Believe it or not, a warm embrace might even help you 4 getting sick this winter. In a recent study 5 over 400 health adults, researchers from Carnegie Mellon University in Pennsylvania examined the effects of perceived social support and the receipt of hugs 6 the participants’ susceptibility to developing the common cold after being 7 to the virus .People who perceived greater social support were less likely to come 8 with a cold ,and the researchers 9 that the stress-reducing effects of hugging 10 about 32 percent of that beneficial effect. 11 among those who got a cold, the ones who felt greater social support and received more frequent hugs had less severe 12 . “Hugging protects people who are under stress from the 13 risk for colds that’s usually 14 with stress,” notes Sheldon Cohen, a professor of psychology at Carnegie. Hugging “is a marker of intimacy and helps 15 the feelin g that others are there to help 16 difficulty.” Some experts 17 the stress-reducing , health-related benefits of hugging to the release of oxytocin, often called “the bonding hormone” 18 it promotes attachment in relationships, including that between mother and their newborn babies. Oxytocin is made primarily in the central lower part of the brain , and some of it is released into the bloodstream. But some of it 19 in the brain, where it 20 mood, behavior and physiology. 1．[A] Unlike [B] Besides [C] Despite [D] Throughout 2．[A] connected [B] restricted [C] equal [D] inferior 3．[A] choice [B] view [C] lesson [D] host 4．[A] recall [B] forget [C] avoid [D] keep 5．[A] collecting [B] involving [C] guiding [D] affecting 6．[A] of [B] in [C] at [D] on 7．[A] devoted [B] exposed [C] lost [D] attracted 8．[A] across [B] along [C] down [D] out 9．[A] calculated [B] denied [C] doubted [D] imagined 10．[A] served [B] required [C] restored [D] explained 11．[A] Even [B] Still [C] Rather [D] Thus 12．[A] defeats [B] symptoms [C] tests [D] errors 13．[A] minimized [B] highlighted [C] controlled [D] increased
2017年考研数学三考试大纲 考试科目：微积分、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 微积分约56% 线性代数约22% 概率论与数理统计约22% 四、试卷题型结构 单项选择题选题8小题，每小题4分，共32分 填空题6小题，每小题4分，共24分 解答题（包括证明题）9小题，共94分 微积分 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和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、了解数列极限和函数极限（包括左极限与右极限）的概念 6、了解极限的性质与极限存在的两个准则，掌握极限的四则运算法则，掌握利用两个重要极限求极限的方法 7、理解无穷小量的概念和基本性质，掌握无穷小量的比较方法．了解无穷大量的概念及其与无穷小量的关系 8、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 9、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经济意义函数的可导性与连续性之间的关系平面曲线的切线与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、反函数和隐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'Hospital）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与最小值