题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-61875.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-66383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-66383.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-91655.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-10827.png)
(Ⅱ)若在区间(0,e]上至少存在一点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043851-15435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043851-95552.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-66383.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-10827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043851-58323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043851-70902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043851-42595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-10827.png)
(II)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043852-57639.png)
解析
试题分析:(I)应用导数研究函数的单调性及极值的基本题型,利用“表解法”清晰明了.
(II)解答本题的关键是,首先将问题转化成“若在区间(0,e]上至少存在一点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043851-15435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043852-58230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-10827.png)
应用分类讨论思想,就
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043852-92633.png)
试题解析:(I)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043852-29752.png)
当a=1,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043853-18277.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043853-26754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043851-42595.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-10827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043853-63551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-10827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043853-27174.png)
![]() | (0,1) | 1 | ![]() |
![]() | - | 0 | + |
![]() | ↘ | 极小值 | ↗ |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043851-42595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-10827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-10827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043851-58323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043851-70902.png)
(II)因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043854-99346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043854-61790.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043853-26754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043852-92633.png)
若在区间(0,e]上至少存在一点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043851-15435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043851-95552.png)
其充要条件是
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-10827.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043852-92633.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043854-51983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043854-38031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043855-79542.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-10827.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-10827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043855-74895.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043855-83484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043855-18881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043855-14202.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043852-92633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043856-93015.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043856-52727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043856-74440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043856-24733.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-10827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043857-14603.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-10827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043857-14603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043855-74895.png)
显然,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-10827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043857-14603.png)
②若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043857-40823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043857-16388.png)
![]() | (0,![]() | ![]() | (![]() |
![]() | - | 0 | + |
![]() | ↘ | 极小值 | ↗ |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043850-10827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043857-14603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043857-46259.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043857-46259.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043858-11940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043858-63753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043858-17161.png)
综上,由(1)(2)可知:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043852-57639.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043841-99252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043841-11770.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043841-34163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043841-50318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043841-19474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043842-78951.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043823-55228.png)
(1)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043823-51453.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043824-12204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043824-38132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043824-69955.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043824-34215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-91734.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043825-78009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-91437.png)
(1)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-49008.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-35551.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-29575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043806-75933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043807-80843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043758-81213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043758-16277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043758-38751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043758-64206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043758-12258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043759-58927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043758-81213.png)
①
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043759-45422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043759-45223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043759-91389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043800-92786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043800-76720.png)
A.2 | B.3 | C.4 | D.5 |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043753-30012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043753-73944.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043753-33343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018043753-52592.png)
最新试题
- 1在数轴上表示不等式的解集,正确的是[ ]ABCD
- 2阅读下面这首诗,回答问题。(8分)乙亥岁除渔梁村黄公度年来似觉道途熟,老去空更岁月频。爆竹一声乡梦破,残灯永夜客愁新。云
- 3阅读下面的文言文,完成小题。白,字太白,山东人。母梦长庚星而诞,因以命之。十岁通五经,自梦笔头生花,后天才赡逸。喜纵横,
- 4小桥(1)横在山之陬,水之滨,卧在江南烟雨里,北国迷茫风雪中。无论石拱的,木架的,无论藤编的,舟浮的,简素、玲珑、野朴,
- 5— How did you find the film Transformers 3 (变形金刚3)? — _____
- 6年轻人喜欢染发,染发时会用到一种着色剂-对苯二胺,它是一种有毒的化学药品,有致癌性,会对染发者的身体带来伤害,下列关于对
- 7近来,刘娟的父母关系不和,经常吵架。父亲每天晚上都喝得醉醺醺的,回来之后就拿女儿出气,经常打骂刘娟。这样的情况已经持续半
- 8两个轻小物体相互吸引,则:[ ]A.两个物体必定带同种电荷 B.两个物体必定带异种电荷 C.两个物体都不带电 D
- 9下列各图中,A、B两点的电场强度相同的是( )A.B.C.D.
- 10(1)化学与我们的生活息息相关.请用化学用语完成下列填空:①天然气的主要成分______;②水银温度计中的液态金属___
热门考点
- 1光球层和色球层分别出现的太阳活动是( )A.黑子和耀斑B.耀斑和日珥C.黑子和日珥D.耀斑和黑子
- 2一群处于n=3激发态的氢原子向低能级跃迁,发出的光垂直照射到一块截面为三角形的玻璃棱镜的AB面上,能从AC面出射的光线将
- 3在平原地区,建设高速铁路时多采用高架的方式,其目的主要是A.减少噪音扰民B.较少地占用耕地C.缩短运营里程D.保护野生动
- 4下列词语中加粗的字,读音没有错误的一组是[ ]A.滑稽(jī)辖制(xián)悖乎(bèi)否极泰来(fǒu)
- 5遭到广泛质疑的号称“神仙道长”、“养生大师”的重庆缙云山绍龙观住持李一,造假履历,传授虚假养生秘诀,骗取钱财,把简单的魔
- 6某校准备参加2004年全国高中数学联赛,把10个名额分配给高三年级8个班,每班至少1人,不同的分配方案有______种.
- 7a为声源,发出声波;b为接收者,接收a发出的声波。a、b若运动,只限于在沿两者连线方向上,下列说法正确的是(
- 8The purpose of the newly-invented robots which can help bath
- 9下列句子中,加点的熟语使用正确的一项是( )A.某国虽然年年搞军演,次次都试射导弹,但总是屡试不爽,不是发射
- 10下列词语中没有错别字的一组是( )A.景仰利欲熏心汪洋咨肆一言以蔽之B.蜂拥贸然行事戛然而止万变不离其宗C.松弛骨鲠在喉