名校
解题方法
1 . 已知函数
.
(1)证明:
;
(2)设函数
,若
恒成立,求
的最小值;
(3)若方程
有两个不相等的实根
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc36a3c21811a9754a537062a73f43e6.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e799e937076aa5a7dcd51cdc0f40f6b0.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5706e65074de43ba1d3b0f5861646e1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa18838a13fda4e45612c32cdf98b71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f98def21c9ea5780553a3dfb46d455f.png)
您最近一年使用:0次
2 . 已知函数
(a为常数).
(1)求函数
的单调区间;
(2)若存在两个不相等的正数
,
满足
,求证:
.
(3)若
有两个零点
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efa8ea75ca2f775085b1838bef2c641d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若存在两个不相等的正数
![](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/abf7c745cd02f4620a175cf00ec85e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3da00fe1feafb42d7e2254dd5f8589.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.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/40c67a34394380636fdf4b882ce28d40.png)
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2023-12-30更新
|
1247次组卷
|
10卷引用:黑龙江省哈尔滨市第六中学校2022-2023学年高三上学期期中数学试题
黑龙江省哈尔滨市第六中学校2022-2023学年高三上学期期中数学试题(已下线)模块五 专题6 全真拔高模拟6(已下线)5.3 导数在研究函数中的应用(练习)-高二数学同步精品课堂(苏教版2019选择性必修第一册)福建省宁德市福安市福安一中2023-2024学年高三上学期10月月考数学试题(已下线)模块三 大招24 对数平均不等式(已下线)模块三 大招10 对数平均不等式重庆缙云教育联盟2024届高三高考第一次诊断性检测数学试卷(已下线)模块2专题7 对数均值不等式 巧妙解决双变量练(已下线)专题6 导数与零点偏移【练】(已下线)专题16 对数平均不等式及其应用【讲】
名校
3 . 已知曲线
在点
处的切线为
.
(1)求直线
的方程;
(2)证明:除点
外,曲线
在直线
的下方;
(3)设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1026c00ff9d78946b4984d09de77995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f84134092f31767ff9f7e8200a79fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)证明:除点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa83d5be9b28fcfce25c9bfca0d3d4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab873c4173a3992c043fbf32cab4d8c.png)
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2024-04-26更新
|
1313次组卷
|
4卷引用:云南省开远市第一中学校2023-2024学年高二下学期期中考试数学试题
名校
4 . 已知函数
.
(1)求曲线
在点
处的切线方程;
(2)设
,求证:当
时,
;
(3)对任意的
,判断
与
的大小关系,并证明结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38e2cfb9e16f2f5d7a1e9a7590dd073.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585de67a3fc494297d375d339af6d153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b79ae1ceee652b06fc889607ff3f1df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa38ca27c6c0c40d5e36b2ae4fb7ba7.png)
(3)对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c975a637794e6be6dd95e1e1ba12620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa9fca7538f46d9d2b4429dd085ac78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
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2023-06-18更新
|
428次组卷
|
2卷引用:北京市大兴区2022-2023学年高二下学期期中考试数学试题
解题方法
5 . 已知函数
,其中
.
(1)讨论
的极值,当
的极值为2时,求
的值;
(2)证明:当
时,
;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26d9147e60a99e9b9ce7c7e7f1bdf17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4138f6987cd2ee9e56b2ac80e84f9e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1898b8d7f9852b531bab793d7ed14526.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82653f6cd7195e117b82512bfe5c75e.png)
您最近一年使用:0次
名校
6 . 已知函数
与
有相同的最大值(其中e为自然对数的底数).
(1)求实数
的值;
(2)证明:
,都有
;
(3)若直线
与曲线
有两个不同的交点
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a889ce5a83ca52532baee3ab4ab405.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eada1c2d3a9e1745f3bdf04d160c80a.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/216a513198e3c6a9f900f4b24433788d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
(3)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9034a9453ec63e9486fa791b869ac54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f4eff3125c5e63a994ba1ad5be58e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/587a0bc676e5c9484e9b6183aa788f5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/124f539f92bfa4ddaaeb00496c386186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ec20f97a849f48988a3307945fb6df4.png)
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2022-10-12更新
|
462次组卷
|
2卷引用:天津市第二十中学2023-2024学年高三上学期期中数学试题
名校
解题方法
7 . 对于正实数
有基本不等式:
,其中
,为
的算术平均数,
,为
的几何平均数.现定义
的对数平均数:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b454c722316d2e530e935987adcb81.png)
(1)设
,求证:
:
(2)①证明不等式:
:
②若不等式
对于任意的正实数
恒成立,求正实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1f53d48a9ad9f88f4b3c14f2637d3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b0bcbf744c3da99e6488f8e66cb8c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee128ea692363f9a7b0cf0958e5f74e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b9514b5e245327b05261ac9a946063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b454c722316d2e530e935987adcb81.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/855eaf612ac4e4505948ee0a1c3c080e.png)
(2)①证明不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8188a2ffd328c07a359ea9be8102a70.png)
②若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0a551c4d6741cae6d513122166db90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aff93e03b22c6053550486ea4e911c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2022-05-11更新
|
493次组卷
|
6卷引用:湖南省长沙市明德中学2021-2022学年高二下学期期中数学试题
名校
8 . 设l为曲线C:
在点
处的切线.
(1)求l的方程;
(2)证明:除切点
之外,曲线C在直线l的下方;
(3)求证:
(其中
,
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7071d5bd0a9c62c880700cb16826df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
(1)求l的方程;
(2)证明:除切点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/989c2c26e0faafc868b46ee921721cd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
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2020-03-05更新
|
937次组卷
|
2卷引用:四川省成都市第七中学2018-2019学年高二下学期期中考试数学(理)试题
名校
9 . 已知函数
.
(1)当
时,求证:
;
(2)当
时,若不等式
恒成立,求实数
的取值范围;
(3)若
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41f0a059d02f88033d4c46fbe648ba2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bc1807f5f5784e75c4e5e6df17f3ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e2d7a7b5ef6de479ac02b04965245d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a154aa77357cb73cbcd37275d873a324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e2d7a7b5ef6de479ac02b04965245d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d9c89d2cd1fb46b1e71ad10227c098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a375205425cf8092535bcc485646fdc3.png)
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2019-03-30更新
|
1687次组卷
|
8卷引用:【全国百强校】安徽省屯溪第一中学2017-2018学年高二下学期期中考试数学(理)试题
名校
10 . 已知函数
.
(1)当
时,若
有两个零点,求实数
的取值范围;
(2)当
时,若
有两个极值点
,求证:
;
(3)若
在定义域上单调递增,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f56de34e94fca24318fa9976625fadb5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41af6fa656b452c5f92816790b499201.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51442bf0ef97e173588b54ee77db26b5.png)
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