名校
1 . 已知
,函数
.
(1)当
时,求
的单调区间;
(2)当
时,设
的导函数为
,若
恒成立,求证:存在
,使得
;
(3)设
,若存在
,使得
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9fef330410912ad36677dbf8549b7f7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0953444691256f713639f4ded91ff306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990ea00761500cbd2a51283a2f443421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c72d250a079379c5175693c165248c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90f8f8ab529ff605ee0c00e551a01622.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ae80746de8e491dcb8df4b1c42dbea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fd7af568e3d9f444beb0ff41426477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478052f005a72e660f55b439e77955dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c247baa451cd7868d97daa7103085ae.png)
您最近一年使用:0次
2024-06-11更新
|
260次组卷
|
5卷引用:天津市部分区2023届高三二模数学试题
天津市部分区2023届高三二模数学试题(已下线)第九章 导数与三角函数的联袂 专题三 含三角函数的恒成立问题 微点3 三角函数的恒成立问题(三)新疆维吾尔自治区伊宁市第三中学2024届高三下学期3月月考数学试题(已下线)专题6 导数与零点偏移【练】(已下线)2024年天津高考数学真题平行卷(提升)
2 . 若函数
的图象上的若干个不同点处的切线互相重合,则称该切线为函数
的图象的“自公切线”,称这若干个点为函数
的图象的一组“同切点”例如,如图,直线
为函数
的图象的“自公切线”,
,
为函数
的图象的一组“同切点”.
在
处的切线为它的一条“自公切线”,求该自公切线方程;
(2)若
,求证:函数
,
有唯一零点,且该函数的图象不存在“自公切线”;
(3)设
,函数
,
的零点为
,求证:
为函数
的一组同切点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.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/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/556995a9d28d7755aa28d18fcdf82386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e2d0b8cd2c080211babbefe92a8969b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4ee7e0a6461d1d6636e376bfa9b275.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe02c554d7141801d82ae5b12a8ad8e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4757efc8199c12b32f07b11d4ddb9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce603aa3abcb61750d2191aaa13dddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/309b41172ad8049ec30a81c6fdc1e502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/556995a9d28d7755aa28d18fcdf82386.png)
您最近一年使用:0次
3 . 已知函数
及其导函数
满足
,且
.
(1)求
的解析式,并比较
,
,
的大小;
(2)试讨论函数
在区间
上的零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee97d8c31054a7150199058bc7b45cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a53de2e60c85b2044ed87efc5b76b8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcd31560d1ff739f03666ce818500e41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab30faa78cc53c104f61b1cd906c365.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d331c2ced600e822884ad16bb13c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9471096d0a3ab27dcc8dec3311ec0234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e63ecfc3c4165229e5538bd3d5d6d44.png)
(2)试讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882ea00f2413de1020f2368786c6dbd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55cfcbb5c5950e18a8452b38bb17036.png)
您最近一年使用:0次
名校
4 . 已知函数
.
(1)若
,讨论
的零点个数;
(2)若
是函数
(
为
的导函数)的两个不同的零点,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a441ed40dca1a0f8c5ed0253d1ca300.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab42358409a44ea7a55fe532fe66ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b550cb121a3346f8d46b7f7ee2117d5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380beb181ed0a48cc486131bba4a4c46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d106beb9c7a567f35e7f3407f41c963c.png)
您最近一年使用:0次
2024-03-27更新
|
615次组卷
|
3卷引用:河南省焦作市2024届高三第二次模拟考试数学试题
名校
5 . 函数
,
,
.已知
有极小值
,
有极小值
.
(1)求
的取值范围;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ea83afd86cb24bb191956d6dd68106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427352f1d09e1f6ee7c54cadaca64906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f371d431b6c91972b742c426c8a81ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
6 . 多元导数在微积分学中有重要的应用.设
是由
,
,
…等多个自变量唯一确定的因变量,则当
变化为
时,
变化为
,记
为
对
的导数,其符号为
.和一般导数一样,若在
上,已知
,则
随着
的增大而增大;反之,已知
,则
随着
的增大而减小.多元导数除满足一般分式的运算性质外,还具有下列性质:①可加性:
;②乘法法则:
;③除法法则:
;④复合法则:
.记
.(
为自然对数的底数),
(1)写出
和
的表达式;
(2)已知方程
有两实根
,
.
①求出
的取值范围;
②证明
,并写出
随
的变化趋势.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9265c54f2a96bf290388484cfd0ff47a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c75f7dcce2b59c10237868c6715ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c137b971df3492a2001085d98706801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1343590f4aaf6b9e3f3c200e318bfea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43887f94250f6c073e144f2ae39b3021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8baf79cfbc5cc29029ca66632c20775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf1c89ff75dc38ce474a01c4932f8c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff01089fbfd66ae3411b15e54f7a9120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef134baac9bb96324f585c5e532cbefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09df69561e70f6d8a66d32f7ffa8a60d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272a7f552e7d99ab3756c1d4e64fc355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9e8e03d12633cfe6858b8c85047100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d6ee0cf2632c76087f5bce01358ef8.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b0e3a7c0dc3c1143610f60a0fd884f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1343590f4aaf6b9e3f3c200e318bfea0.png)
(2)已知方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a7df955fc17e92fd86302f8c34664a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
①求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b18df306af443a02bf538cfc517d4a50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-02-21更新
|
1087次组卷
|
3卷引用:广东省广州市华南师范大学附属中学2024届高三上学期数学周测试题(12)
广东省广州市华南师范大学附属中学2024届高三上学期数学周测试题(12)(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编江苏省海安高级中学2023-2024学年高二下学期第二次月考数学试题
名校
7 . 已知函数
.
(1)当
时,求
的极值;
(2)若存在实数
,满足
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8d0dffe17c575a4feb86c28d97182a7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e1c602ee00edc5ef54b0e552fec94a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a416908781159f632dfdbcdd50353d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c40639f6df6efc0e1e73ab07b2d8c67.png)
您最近一年使用:0次
2024-02-21更新
|
1061次组卷
|
4卷引用:吉林省长春市朝阳区吉大附中实验学校2024届高三下学期开学考试数学试题
吉林省长春市朝阳区吉大附中实验学校2024届高三下学期开学考试数学试题福建省名校联盟全国优质校2024届高三大联考数学试卷(已下线)5.3.2课时2函数的最大(小)值 第三练 能力提升拔高四川省绵阳市三台中学校2024届高三下学期第二学月测试理科数学试题
2024·全国·模拟预测
名校
解题方法
8 . 已知函数
,其中
为自然对数的底数.
(1)当
时,求函数
在区间
上的极值;
(2)当
时,函数
的正零点从小到大依次为
.证明:
①
;
②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f4227dc3811664afa9857a689425c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/113cc2eb1633f22868d0f178b7dbdd74.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8fbb2f793b78744fab05981d13e1f2.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99794f486ec1e9476eae89c325196479.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f0bfb1225626e9cddc09e6f3745422f.png)
您最近一年使用:0次
9 . 设
,满足
.
(1)证明:若
,则当
时,
.
(2)若存在
满足
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e761714f6940c2c06c5750e2ed80cc4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fbd27b6b4143c730ab9d36393a5fe14.png)
(1)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c61cfbfd3bf888856b7dc9b2a84c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac247d375e0da7fddafad1aa8186aa51.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4439c7de7291f79def06d548603de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa3205b1df826d63914dcb55bb3ab43.png)
您最近一年使用:0次
解题方法
10 . 已知函数
,
为实数.
(1)若
在
上单调递增,求实数
的取值范围;
(2)若
.
①证明:
既有极大值又有极小值;
②若
,
分别为函数
的极大值和极小值,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/363aaad7b209645176bb88f91765218b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/113cd76ec8016056cda65fea47359299.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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