1 . 已知函数
(e是自然对数的底数).
(1)当
时,求函数
在点
处的切线方程;
(2)当
时,
①求证:函数
存在唯一的极值点
;
②在①的条件下,若
且
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ddd575cc364fce97abc72303089b6b5.png)
(1)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/5828873f8369183faf71181cda5b61d2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db8f867196410e2828e2bbd3183b02d.png)
①求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
②在①的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36825543013336c9df727bc51ff62c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da9cabe1ba5acf13a43ba47b290d9729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fef48ef60798be483aa190c3418e77f.png)
您最近一年使用:0次
名校
2 . 函数
,函数
若函数
恰有2个零点,则实数a的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1b9b3f6d704232c6920c368e33b9ae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13381f2109fad6335d2a738bc8b4daf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ec7987f88ec5e973e7771fefcc5e3e5.png)
您最近一年使用:0次
2024-01-22更新
|
715次组卷
|
6卷引用:天津市八校联考2023-2024学年高三上学期期末质量调查数学试卷
天津市八校联考2023-2024学年高三上学期期末质量调查数学试卷(已下线)信息必刷卷01(天津专用)福建省莆田市莆田第一中学2024届高三上学期第一次调研数学试题(已下线)第二讲:方程与函数思想【练】(已下线)高二下学期第一次月考填空题压轴题十四大题型专练-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第三册)(已下线)模型9 分段函数含参的零点模型(高中数学大模型)
名校
3 . 黎曼猜想是解析数论里的一个重要猜想,它被很多数学家视为是最重要的数学猜想之一.它与函数
(
,s为常数)密切相关,请解决下列问题.
(1)当
时,讨论
的单调性;
(2)当
时;
①证明
有唯一极值点;
②记
的唯一极值点为
,讨论
的单调性,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/755d78f27a96bf14b96dff9913851df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b862659eee15ac003d2d2c53d9abbf5c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b366d99460274e9ab2187c11af8a6372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f15bcd4917a74ec6f505f0e10833a7f.png)
①证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
②记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/010dec4fc2df0b58992eb4515cd13eff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/010dec4fc2df0b58992eb4515cd13eff.png)
您最近一年使用:0次
2024-01-15更新
|
2845次组卷
|
9卷引用:天津市第一中学滨海学校2024届高三第六次学业水平质量调查数学试卷(开学考)
天津市第一中学滨海学校2024届高三第六次学业水平质量调查数学试卷(开学考)2024届广东省惠州市大亚湾区普通高中毕业年级联合模拟考试(一)数学试卷2024届广东省大湾区普通高中毕业年级联合模拟考试(一)数学试题湖南省长沙市长郡中学2024届高三一模数学试题(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吉林省通化市梅河口市第五中学2024届高三下学期一模数学试题(已下线)专题2 导数与函数的极值、最值【练】辽宁省锦州市某校2023-2024学年高三下学期考前测试数学试卷(A)河南省信阳市新县高级中学2024届高三考前第七次适应性考试数学试题
名校
4 . 已知函数
,(
为自然对数的底数).
(1)求曲线
在
处的切线方程
(2)若不等式
对任意
恒成立,求实数
的最大值;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8294bb352cef50b3a8961fcf0474aa6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e69e0bad37111c1169746941ac1f833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f47dd5fc03cf0d593fcf67b5d18d1c2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f2416d1f75a45a314331146550832e.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bac345bdfae4f716fde3946ed3708c2.png)
您最近一年使用:0次
名校
5 . 已知函数
,
.
(1)讨论
的单调性;
(2)当
时,若
的极小值点为
,证明:
存在唯一的零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b62446c55270cc760f268c60de71a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3002ad1638f25e355d70d5ab63e637f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1d9ff5befe43e47d35e5662859f0f18.png)
您最近一年使用:0次
2024-01-02更新
|
1051次组卷
|
4卷引用:高三数学开学摸底考(天津专用)
(已下线)高三数学开学摸底考(天津专用)广东省深圳实验、湛江一中、珠海一中三校2024届高三上学期12月联考数学试题江苏省苏州市相城区南京师大苏州实验学校2024届高三上学期期末模拟数学试题(已下线)模块三 大招11 隐零点代换
6 . 已知函数
,
,
.
(1)若曲线
在点
处的切线的斜率为3,求
的值;
(2)当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1e123a2b615be0baeef83bd218bce.png)
,函数
有两个不同零点,求m的取值范围;
(3)若
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17a30c71f953b3034c53ceb21a2d018a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55506fc48681be9458f6b9cf443166ea.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1e123a2b615be0baeef83bd218bce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ce23def379af825c9af9556bfe68e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae22a99a838d7706ca363774d399773.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e81b4aac721bcd4a49593b48a28a8f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/326588fbba1f82a9e0bed87884eca277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
7 . 已知函数
,其中
.
(1)求曲线
在
处的切线方程
,并证明当
时,
;
(2)若
有三个零点
,且
.
(i)求实数
的取值范围;
(ii)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f7bac7520fa44f299a861781626472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8821abd8dda8b7cbfec152700ef79f4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
(i)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb8404a0443abc179871b8ebefbf9fb.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数,其中
是自然对数的底数.
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5815ab5cc9753e2e6415a97d6f4d3ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
您最近一年使用:0次
名校
解题方法
9 . 若函数
在区间
上有零点,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac85c110a06ecba9f46abbb998ccd32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c925be255ca736a53b24d13ddede1a86.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
10 . 已知函数
,
,
.
(1)若函数
在
处的切线与直线
垂直,求实数k的值;
(2)若
恒成立,求实数k的取值范围;
(3)设
,证明:当
时,函数
存在唯一的极大值点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31462ab022258f10eb566a51461251a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b508b873789c7cc865c0dc73ba6e274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51ace462e64d4cb4f7f50c42f70bfae.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e8f77e3876694978a22975eff397375.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bdf04f070224d193aaa2d0b13b96d48.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb48434bdcafb5e084fc0b6396cb9469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91869b1b8e92295828a336e7a1373b2.png)
您最近一年使用:0次
2023-06-14更新
|
616次组卷
|
2卷引用:天津市武清区杨村第一中学2023届高三下学期第一次热身练数学试题