1 . 已知函数
.
(1)求
的单调区间;
(2)证明:
;
(3)若
,且
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e50ead3dafa710129bd59b727bfd756.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29772ffc1a200fb6cd2283aef27e2874.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea134f599285e3d32d2ab3e7186990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225a93c53ca692b1e0a7c9809bbb5326.png)
您最近一年使用:0次
2 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)当
时,求函数
的单调区间;
(3)在(2)的条件下,当
时,
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e5101ed57406f68a0a9372bbd007a0.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/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)在(2)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/998485ffeb46a0412ff1a0f814429257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52109b598fb211d3c8ecc3f7718118cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
3 . 已知函数
,
.
(1)讨论函数
的单调性;
(2)若
=0,求
的值;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a136afa15ea25aba12111fd15f6340f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97d7daa713ad26b1537eb66a0a35db9c.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d0532bf8ea573af0bc5bbda9e52154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08649488c4b6e75ded28491787ef7558.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22385a460e5c54a3736e2eccd185c418.png)
您最近一年使用:0次
2023-10-22更新
|
505次组卷
|
12卷引用:天津市河北区2022届高三下学期总复习质量检测(一)数学试题
天津市河北区2022届高三下学期总复习质量检测(一)数学试题江西省八所重点中学2021届高三4月联考数学(理)试题(已下线)精做06 函数与导数-备战2021年高考数学(理)大题精做(已下线)2021年高考数学(理)押题预测卷(新课标III卷)01(已下线)【新东方】高中数学20210513-003【2021】【高二下】江苏省苏州市第一中学2020-2021学年高二下学期期中数学试题(已下线)专题4.15—导数大题(构造函数证明不等式2)-2022届高三数学一轮复习精讲精练重庆市长寿中学2020-2021学年高二下学期第一次月考数学试题(已下线)专题2.16 导数-不等式的证明-2021年高考数学解答题挑战满分专项训练(新高考地区专用)北京市广渠门中学2024届高三上学期开学考数学试题天津市汇文中学2023-2024学年高三上学期10月月考数学试题北京市海淀实验中学2024届高三上学期10月月考数学试题
名校
解题方法
4 . 已知函数
,
.
(1)讨论函数
的单调区间;
(2)当
时,直线
是曲线
的切线,求
的最小值;
(3)若方程
有两个实数根
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6365876ce2de96a32ca13841a92824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c80e0a0f1b839ec70ed1028c6665a89.png)
(3)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e255b987904e9442668dc3fdc1a6ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69f02b52c7928235fe5e25b4c5ca4ebc.png)
您最近一年使用:0次
名校
5 . 设
,
.
(1)当
时,求曲线
在点
处的切线方程;
(2)若对
,有
,求
的取值范围;
(3)设
在
中有两个零点
,
,证明:
随着
的增大而减小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e91d5400772001006982384a78ce268b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848c33e3506416358d9f0d3ee66f67a9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348551d9ea36d82fab80ae54df9d6c89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f4eff3125c5e63a994ba1ad5be58e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3907da01aa2971e05262ecf58bafe27d.png)
(2)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311ff26a0cb99d45aaa85ec23a5505f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b817338735d4c23394d6601a7ea4ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f1b4e037116928fd60f5892a211819.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b0305f69331f9bbd5bbcecfc2a694c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95d4b8e7713f727e2c5d8cc30e50e28d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1019d4ad2e3fb4a7abb66e0e9e55b556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
您最近一年使用:0次
名校
解题方法
6 . 设函数
,其中
.
(1)若
,求
的单调区间;
(2)若
,
(ⅰ)证明:
恰有一个极值点;
(ⅱ)设
为
的极值点,若
为
的零点,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f30983749e441d75a4906986e142ac5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848c33e3506416358d9f0d3ee66f67a9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b08650d86e207ceded5c8abbfd2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f42fac6e4c5c1b5834bca8f1e8163b.png)
(ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
(ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/015740ce0b7022cf0a5503747c020999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12a4eecd249473a831d0ee472470240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fbfc2b58374e9608973ce3b108726b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b8433690ac98d370f532e71c3383f4.png)
您最近一年使用:0次
2022-10-18更新
|
574次组卷
|
4卷引用:天津外国语大学附属外国语学校2021-2022学年高三上学期结课检测数学试题
天津外国语大学附属外国语学校2021-2022学年高三上学期结课检测数学试题(已下线)北京市西城区2022届高三二模数学试题变式题16-21江苏省常州高级中学2023届高三上学期1月月考数学试题上海市行知中学2024届高三上学期10月月考数学试题
7 . 已知函数
,若函数
恰有三个零点,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa1791f8a85604d23a3df86440bc3563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7acf0690a085ef9393fac6ad08fbd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-09-27更新
|
745次组卷
|
4卷引用:天津市河北区2022-2023学年高三上学期期末数学试题
名校
8 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36da216de22e8ea3f1f3c5c1ce4e4f56.png)
(1)求曲线
在点
处的切线方程;
(2)求函数
的单调区间和极值;
(3)若
,
对任意的
恒成立,求m的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36da216de22e8ea3f1f3c5c1ce4e4f56.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d4999a846dafaf3fe0ef8708633b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bddc103dd6591a8f0d4146ed287e16be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac0c4f74d16d30a8799b03b41460cfa.png)
您最近一年使用:0次
2022-03-13更新
|
1703次组卷
|
6卷引用:天津市河北区2021-2022学年高三上学期期末数学试题
天津市河北区2021-2022学年高三上学期期末数学试题天津市外国语大学附属外国语学校2021-2022学年高二下学期期中数学试题(已下线)临考押题卷02-2022年高考数学临考押题卷(天津卷)北京市十一学校2021-2022学年高二下学期第3学段教与学诊断(期中)数学试题(已下线)高二数学下学期期末精选50题(压轴版)-2021-2022学年高二数学考试满分全攻略(人教A版2019选修第二册+第三册)重庆市渝北区礼嘉中学2021-2022学年高二下学期期末模拟数学试题
名校
9 . 已知函数
.
(1)已知
为
的极值点,求曲线
在点
处的切线方程;
(2)讨论函数
的单调性;
(3)当
时,若对于任意
,都存在
,使得
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b72020623b782fe41306135d39ff43.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c74f6363d928d201b609514f3d6b2c.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce655a13dea9309f8ed84036ba293aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71fbd2ce77a53d084eaeb73c3367c758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d701701514d29d22d56e8a35f797d267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c45b3031cbe99e5b1d8610976391076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968f416acf5802ec526df006edf6e3f6.png)
您最近一年使用:0次
2021-06-04更新
|
2298次组卷
|
9卷引用:天津市第二中学2022届高三下学期5月线上测试数学试题
天津市第二中学2022届高三下学期5月线上测试数学试题天津市武清区杨村第一中学2021届高三下学期高考热身训练一数学试题天津市武清区英华国际学校2021-2022学年高三上学期第一次月考数学试题(已下线)第10讲 双变量不等式:中点型-突破2022年新高考数学导数压轴解答题精选精练天津市第一中学滨海学校2022届高三下学期第一次质量调查数学试题天津市南仓中学2022-2023学年高三上学期第一次教学质量过程性监测与诊断数学试题天津市静海区第一中学2021届高三下学期二模数学试题天津市第四十七中学2022-2023学年高三上学期第二次阶段性学习检测(期末)数学试题(已下线)重难点突破06 双变量问题(六大题型)
名校
10 . 已知函数
,
.
(1)若
,求
的最大值;
(2)若函数
,讨论
的单调性;
(3)若函数
有两个极值点
,
(
),求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e809e64e1ce894b194d4406c7e781604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8bc2441a9c398d1d65419e51c08a8f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca4be345087f993a4078e16c16608e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bec54e1cb8e24718af2ceab42bc31e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee6183d1f5f283b815f517d4fe2e275f.png)
您最近一年使用:0次
2021-05-08更新
|
591次组卷
|
4卷引用:天津市河北区2022届高三下学期总复习质量检测(二)数学试题
天津市河北区2022届高三下学期总复习质量检测(二)数学试题黑龙江省哈尔滨第九中学2019-2020学年度上学期高三第二次月考数学理试题陕西省汉中市2021届高三下学期第二次检测理科数学试题(已下线)第四章 导数专练8—双变量与极值点偏移问题(2)-2022届高三数学一轮复习