名校
1 . 已知函数
,
,(
是自然对数的底数),
.
(1)若
是
上的单调递增函数,求
的取值范围;
(2)若函数
的图象与直线
有且仅有三个公共点,公共点横坐标的最大值为
,求证:
.
(3)当a,b满足什么条件时,
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b736a71d31c5a171ad47e68a9b04f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976581d4a974fe50f9f29d430c1289f2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3331dd8cf4127ffdb2e541115dc118a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082990da1f11a1a7be4fc3935c0d526e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ec8eb92402d57af55813b15578e86c.png)
(3)当a,b满足什么条件时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf9093e67bb937df85711d3ab08fb0d2.png)
您最近一年使用:0次
名校
2 . 设函数
.
(1)当
时,求函数
在点
处的切线方程;
(2)当
时,设
,且
轴,求
两点间的最短距离;
(3)若
时,函数
的图象恒在
的图象上方,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18ef4365413af15c45c7b018ddf69fb0.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e732291816c0f81ee182a45e7388aeca.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e0d1ca30e3c973fa59b4f5f5109cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d928238e1f1677f5f20ed62da87eb04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5031e329aa639664c4671aaed4e07926.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
3 . 若函数
满足:对任意
,都有
,则称函数
具有性质
.
(1)设
,
,分别判断
与
是否具有性质
?并说明理由;
(2)设
函数
具有性质
,求实数
的取值范围;
(3)已知函数
具有性质
,且图像是一条连续曲线,若
在
上是严格增函数,求证:
是奇函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47501e15929024c12d5ad671902b2ef2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d813b99569b5439d685be73ac11cb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/841d74a21ac16e7ae3ef811d931de69d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ff9cda1684eaf1a0debe28b5b8f18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
您最近一年使用:0次
名校
解题方法
4 . 已知函数
.
(1)若
在其定义域上单调递增,求k的取值范围;
(2)证明:对
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/899d99dd040179f0bcb349dd46ed7895.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02efa6f1dc514a278597ed9ccfe42127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beed1d56c2ac4a6ac6da4aca548622e7.png)
您最近一年使用:0次
解题方法
5 . 已知函数
.
(1)若函数
在
上单调递增,求
的取值范围.
(2)若函数
的两个零点分别是
,且
,证明:
①
随着
的增大而减小;
②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554604e4c3bb9fe9e186a43d3e0d5575.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be4c51e13a3011722c8340321ad5a7a5.png)
您最近一年使用:0次
6 . 设函数
,
.
(1)若函数
在区间
是单调函数,求
的取值范围;
(2)设
,证明函数
在区间
上存在最小值
,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e72d04202a2454ec355e223745647b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1949b35560c8950cef4dc7645fb9f7e3.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c76c7bcfb0dd9e2dc2d9717a0fd06c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e5be457a03a2b10ef46c1be2ff87b54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd6a50fe17b747aef94342dcef27b27.png)
您最近一年使用:0次
名校
7 . 已知函数
,
(1)若
与
有相同的单调区间,求实数
的值;
(2)若方程
有两个不同的实根
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe1f1aba23cff181ad85db0443f8576f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60570958966fbc7f957eab87252dba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f03fd662f69ce3e5449c08e00b963194.png)
您最近一年使用:0次
2024-03-22更新
|
670次组卷
|
3卷引用:甘肃省张掖市某校2024届高三下学期模拟考试数学试题
8 . 已知函数
.
(1)若
是
上的单调递增函数,求
的取值范围;
(2)当
满足什么条件时,
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/324fe5b0f9d344069f1fb4a58a84ac5f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5374bfc463f980d9dab1ffda5f59885.png)
您最近一年使用:0次
名校
9 . 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
|
1075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
10 . 设
是定义在
上的函数,若存在区间
和
,使得
在
上严格减,在
上严格增,则称
为“含谷函数”,
为“谷点”,
称为
的一个“含谷区间”.
(1)判断下列函数中,哪些是含谷函数?若是,请指出谷点;若不是,请说明理由:
(i)
,(ii)
;
(2)已知实数
,
是含谷函数,且
是它的一个含谷区间,求
的取值范围;
(3)设
,
.设函数
是含谷函数,
是它的一个含谷区间,并记
的最大值为
.若
,且
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1486d2ae6c7e7904ab47b909039ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adadc4c82ed03710cb917d552ac6e1c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd33dd2e1b404daf7c1cbbf147ab7f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)判断下列函数中,哪些是含谷函数?若是,请指出谷点;若不是,请说明理由:
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65ecb5b1f957213346a78a229314e73f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2323ed90e5321507ae65763db9594b9.png)
(2)已知实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2739d1d7a587d0a327c5b75fcaba9d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7242b2ab643f9470da77e29d043b893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0137d9ccd136186c2fe74a11e42376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f86c67af4135ba55b227485de51d4ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
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5卷引用:上海市浦东新区2024届高三上学期期末教学质量检测数学试题
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