名校
1 . 已知函数
.
(1)求
的最小值;
(2)若
有两个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d103871c024db6a95d08b8865a7605fa.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3卷引用:数学(江苏专用02)
2 . 已知
在
处取得极小值
.
(1)求
的解析式;
(2)求
在
处的切线方程;
(3)求
的极值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc9c2470c624d45fbcc20d18329448c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354c3a283b2b21cc8ac33995aac20a5c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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6卷引用:江苏高二专题03导数及其应用
江苏高二专题03导数及其应用江苏省无锡市运河实验学校2023-2024学年高二下学期期中考试数学试卷(已下线)模块三 专题2 解答题分类练 专题1 导数在研究函数性质中的应用(苏教版)(已下线)模块四 期中重组卷3(江苏苏锡常镇)(苏教版)(高二)(已下线)模块一 专题5 导数在研究函数性质中的应用(2)【高二下人教B版】(已下线)模块三 专题2 解答题分类练 专题4 导数在研究函数性质的应用【高二人教B】
3 . 已知函数
.
(1)求函数
的导函数
;
(2)求函数
单调区间;
(3)若函数
有两个不同的极值点
,记过
两点的直线斜率为
,是否存在实数
,使得
,若存在,求实数
的值;若不存在,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c048088bfb2983b329dcaad0b45712.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e029bc001b49c07d747e8b356bcd72d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b680c9cf0ac2e7aed2f445597eb47446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3卷引用:江苏高二专题03导数及其应用
名校
解题方法
4 . 已知函数
和
的定义域分别是A和B,若函数
和
同时满足下列两个条件:
①对任意的
,都有
或对任意的
,都有
;
②存在
,使得
.
则称
和
互为“依偎函数”,记作
,其中,
叫做“依偎点”.
(1)是否存在
有无数个“依偎点”?若存在,请举例说明;若不存在,请说明理由;
(2)若函数
,
,是否存在k,使得
如果存在,求出k的值;如果不存在,请说明理由;
(3)求证:
,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
①对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a479511a50da604b2fc7398617db8387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b4955c5adc717b7f6f0b975e0724ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a479511a50da604b2fc7398617db8387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43920f5171ed31db2520ef00e4c5fc24.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18165b24e85935b2d036eb6ba4aa0125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099adf32792e7334032a80084e0cb584.png)
则称
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0e49c46c9fb222376736229da4e80b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(1)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0e49c46c9fb222376736229da4e80b.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacd6155ac43dbd8aa73d03740c24af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914a49b0d7aedc593a3e87fbab7c31ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f084386fd408381964398bf8c907a7.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a487acd081800a523a236a1337261e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
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2卷引用:江苏高二专题03导数及其应用
名校
5 . 已知函数
.
(1)讨论
的单调性;
(2)当
恒成立时,求
的取值范围;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fdbd96fac44a76334909df9074d1a97.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/996d9e02187335faf7689f1611ab331f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d9aa7d4c35ca378a4b765eda910d490.png)
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3卷引用:江苏高二专题03导数及其应用
名校
6 . “踩高跷,猜灯谜”是我国元宵节传统的文化活动. 某地为了弘扬文化传统,发展“地摊经济”,在元宵节举办形式多样的猜灯谜活动.
(1)某商户借“灯谜”活动促销,将灯谜按难易度分为
两类,抽到较易的
类并答对购物打八折优惠,抽到稍难的
类并答对购物打七折优惠,抽取灯谜规则如下:在一不透明的纸箱中有8张完全相同的卡片,其中3张写有
字母,3张写有
字母,2张写有
字母,顾客每次不放回从箱中随机取出1张卡片,若抽到写有
的卡片,则再抽1次,直至取到写有
或
卡片为止,求该顾客取到写有
卡片的概率.
(2)小明尝试去找全街最适合他的灯谜,规定只能取一次,并且只可以向前走,不能回头,他在街道上一共会遇到
条灯谜(不妨设每条灯谜的适合度各不相同),最适合的灯谜出现在各个位置上的概率相等,小明准备采用如下策略:不摘前
条灯谜,自第
条开始,只要发现比他前面见过的灯谜适合的,就摘这条灯谜,否则就摘最后一条,设
,记小明摘到那条最适合的灯谜的概率为
.
①若
,
,求
;
②当
趋向于无穷大时,从理论的角度,求
的最大值及
取最大值时
的值.(取
)
(1)某商户借“灯谜”活动促销,将灯谜按难易度分为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6b93dbe5272a5167ff4e2918bec864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)小明尝试去找全街最适合他的灯谜,规定只能取一次,并且只可以向前走,不能回头,他在街道上一共会遇到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578606f2403c782b320a303b139dc626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b00f4eb7f1bd2ccefbabf0c1dfa8f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd266684a38a50f7a7925d4bb5e63e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e69866076dcff686a05e9e91e61e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5a5ce3e0a6cbb682718706600b239c.png)
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3卷引用:专题07 概率与统计综合问题(6类题型)-备战2023-2024学年高二数学下学期期末真题分类汇编(江苏专用)
(已下线)专题07 概率与统计综合问题(6类题型)-备战2023-2024学年高二数学下学期期末真题分类汇编(江苏专用)江苏省海安高级中学、宿迁中学2023-2024学年高三下学期模拟考试数学试卷黑龙江省大庆市实验中学实验二部2024届高三下学期得分训练数学试题(六)
名校
7 . 如图,
是半圆
的直径,
为
中点,
,直线
,点
为
上一动点(包括
两点),
与
关于直线
对称,记
为垂足,
为垂足.
的长度为
,线段
长度为
,试将
表示为
的函数,并判断其单调性;
(2)记扇形
的面积为
,四边形
面积为
,求
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf468f5132e14ee1d8cc766808b11af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e2859a53a15cd08e75e6516489948b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b455b110a30c1533d0a0657e0e48ac33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a14abdcd76e14b2fc1abce40b2b1bfe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b7affe747f630ba39abaaff2a080a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9382f3fa0be7e9180546910d579046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02521cd9fa700ef34feeed81c320211f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)记扇形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161ea3eaa2e28747507c1c0e4a7b39f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d918361b03a48660dbd5987cd7a7a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52e6151dc6ef89bc79b1ca0dc63b291e.png)
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|
276次组卷
|
4卷引用:江苏高二专题03导数及其应用
江苏高二专题03导数及其应用江苏省苏州市2023-2024学年高二下学期4月期中调研数学试题(已下线)模块五 专题4 全真能力模拟4(人教B版高二期中研习)福建省龙岩市上杭一中2023-2024学年高二下学期5月月考数学试卷
名校
8 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)当
时,若函数
有最小值2,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee26dd641236c3ee63622d0ca473c9d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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|
5卷引用:数学(江苏专用01)
(已下线)数学(江苏专用01)(已下线)第二章导数及其应用章末十八种常考题型归类(3)海南省四校(海南中学、海口一中、文昌中学、嘉积中学)2024届高三下学期联考数学试题陕西省西安中学2024届高三模拟考试(七)数学(理科)试题单元测试B卷——第五章 一元函数的导数及其应用
2024高三下·江苏·专题练习
解题方法
9 . 已知函数
,当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6b4fd7ea9ebef26c80081aece3cdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f421939ee855f25927e7570d82c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2868fc8e6dc8e0b15a381649a7bd5532.png)
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