名校
解题方法
1 . 已知函数
.
(1)当
时,
,求
的取值范围;
(2)函数
有两个不同的极值点
(其中
),证明:
;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6268f2fe0dc41d2f6f9931e465ef4cab.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5e895d73fc0b144b0245e730c397391.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bef92ee798393ea59d0d9a73a8272809.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b02c07f3b1fd2ce2218985bacdd0b86.png)
您最近一年使用:0次
2023-02-12更新
|
1027次组卷
|
5卷引用:辽宁省大连市第八中学2022-2023学年高二下学期6月月考数学试题
辽宁省大连市第八中学2022-2023学年高二下学期6月月考数学试题浙江省绍兴市上虞区2022-2023学年高三上学期期末数学试题(已下线)拓展五:利用导数证明不等式的9种方法总结-【帮课堂】2022-2023学年高二数学同步精品讲义(人教A版2019选择性必修第二册)吉林省长春市十一高中2022-2023学年高二下学期第二学程考试数学试题(已下线)模块一 专题5 利用导数证明不等式问题
名校
解题方法
2 . 已知函数
.
(1)求
在区间
内的极大值;
(2)令函数
,当
时,证明:
在区间
内有且仅有两个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56ec2258720b77cd82dc6510acc563b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
(2)令函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1582c12e318db71ef25098e6f8872655.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79e9bca78d1e27e7a72b6125c796f57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
您最近一年使用:0次
2023-01-16更新
|
1254次组卷
|
3卷引用:辽宁省名校联盟2023届高考模拟调研卷数学(三)
名校
解题方法
3 . 已知函数
.
(1)求函数
的最值;
(2)若
恒成立,求实数
的取值范围;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d975f2328f11c8ddbb2f1e814788c85.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf15d5dc12f45c0bacf402c97728124c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350c094513823113225bbb6625529551.png)
您最近一年使用:0次
2022-09-09更新
|
794次组卷
|
3卷引用:辽宁省名校联盟2022-2023学年高三上学期9月联考数学试题
名校
解题方法
4 . 已知函数
.
(1)当
时,试比较
与
的大小;
(2)若斜率为
的直线与
的图象交于不同两点
,
,线段
的中点的横坐标为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c64d70d50cb38406a508aeb1837e11.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca542e78b7d77d008c9c4752afa91a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb19d43bf321e4019573260f189a7fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63d7758a927384c13052ae432c20a23.png)
(2)若斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a193c4c10cbbf7d3a6eca993f8abb5.png)
您最近一年使用:0次
5 . 已知函数
.
(1)求函数
的单调区间;
(2)若存在
使
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7601f3fbac3187f1b10e59ad6eecddb6.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859458471c86ae39e0cc42d2d960d03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9856c91ab017738c26f9e6db0217ef.png)
您最近一年使用:0次
2023-01-04更新
|
805次组卷
|
2卷引用:辽宁省北镇市第三高级中学2023-2024学年高三上学期第二次月考数学试题
名校
解题方法
6 . 已知定义域均为
的两个函数
,
.
(1)若函数
,且
在
处的切线与
轴平行,求
的值;
(2)若函数
,讨论函数
的单调性和极值;
(3)设
,
是两个不相等的正数,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/428d922e63d8a0838da6fdacee919ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2adbf5920ef591644eaa616ccac1e9c3.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974afe1dbd93c458e63daa7564a462ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a94ad3ba506860f8491ae7d7d67e8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
(3)设
![](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/0644fb6750e5c61c2d334b1b0094cbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e8f67fafa098c0e1b1c9394859d4cd0.png)
您最近一年使用:0次
2023-05-21更新
|
1158次组卷
|
5卷引用:辽宁省六校协作体2022-2023学年高二下学期6月联合考试数学试题
辽宁省六校协作体2022-2023学年高二下学期6月联合考试数学试题天津市滨海新区2023届高三三模数学试题(已下线)专题19 导数综合-1天津市北师大静海附属学校2024届高三上学期第三次月考数学试题(已下线)专题12 帕德逼近与不等式证明【练】
名校
解题方法
7 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeea9bb195a844feb2f1806db8259604.png)
(1)当
时,证明:
.
(2)若
有两个零点
且
求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeea9bb195a844feb2f1806db8259604.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090e25106827a537fe83b70f5468153b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
您最近一年使用:0次
2022-12-28更新
|
1385次组卷
|
8卷引用:辽宁省锦州市渤海大学附属高级中学2022-2023学年高三上学期期末考试数学试题
名校
解题方法
8 . 已知函数
,且
.
(1)求实数
的取值范围;
(2)设
为整数,且对任意正整数
,不等式
恒成立,求
的最小值;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0097e221a2fd7333fb0d47e86546ba61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2b790c0ffe766b815ea769920bf5b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac9ea10cc95de77e1a0ad091359e590.png)
您最近一年使用:0次
2023-05-14更新
|
647次组卷
|
4卷引用:辽宁省六校2023-2024学年高三上学期期初考试数学试题
名校
9 . 设函数
,其中
为自然对数的底数.
(1)当
时,讨论函数
在
上的单调性;
(2)当
时,求证:对任意
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0b6ffc19f1678f3cd5a1a2687f3e8f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e445f608e4a7d8535b100c0199a8ecf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/009935dae2483304749bfa46ceb6eecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2143a6cfd3526c4f5795328baa51b0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/563ed1ebb56e33b5c387f3666be28fa9.png)
您最近一年使用:0次
2023-01-01更新
|
599次组卷
|
3卷引用:辽宁省瓦房店市高级中学2022-2023学年高三下学期期初考试数学试题
解题方法
10 . 已知函数
,
(1)若
时,求证:函数
)只有一个零点;
(2)对
时,总有
恒成立,求k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/868b6a84b8ba850245610435aa0bef2d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/765a1076581eeaffdc124f1a1676c10e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8625151f40f341575c1a71992e485188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f5253e0770377a99d6e0ede768fc92.png)
您最近一年使用:0次