名校
1 . 已知函数
,曲线
在点
处的切线方程为y=2
(1)求a,b的值;
(2)当
且
时,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef7a69b6903ffc77b3979bd4c2c1ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(1)求a,b的值;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e30c903d8f8a05332af0b19e7e40df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda75174a7a2f1e32f7d476ebf293a89.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
,若
在
处的切线为
.
(Ⅰ)求实数
,
的值;
(Ⅱ)若不等式
对任意
恒成立,求
的取值范围;
(Ⅲ)设
其中
,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deca3dfec58b2806150dbf5a9e16246a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81cb1f86b640a8744cbaf9f246de1821.png)
(Ⅰ)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(Ⅱ)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/173b541b53300548fda24abcca4a3d50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(Ⅲ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21582e49fdff1be41529bd96abb237e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b974113b04534e6855489aebd8354d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def09e0b149cf236feb036026c437bc7.png)
您最近一年使用:0次
2020-05-20更新
|
872次组卷
|
8卷引用:福建省泉州市第七中学2023-2024学年高二下学期期中数学试卷
福建省泉州市第七中学2023-2024学年高二下学期期中数学试卷河北省石家庄市2019-2020学年高三下学期5月阶段性训练数学(理)试题2020届石家庄市高三年级阶段性训练(理)试题重庆市育才中学2021届高三上学期12月月考数学试题重庆市育才中学2021届高三上学期1月月考数学试题(已下线)第35讲 函数与数列不等式问题-突破2022年新高考数学导数压轴解答题精选精练黑龙江省哈尔滨师范大学附属中学2022-2023学年高三上学期期末考试数学试题(已下线)专题19 导数综合-2
解题方法
3 . 已知
.
(1)证明
在
处的切线恒过定点;
(2)若
有两个极值点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374d913147d7dc157a0bb67244f203a1.png)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
4 . 已知函数
.
(1)当
时,求曲线
在
处的切线方程;
(2)讨论
的单调性;
(3)设
、
为曲线
上的任意两点,并且
,若
恒成立,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26b5bd951dfa97c79aa477529a49ae8a.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/9b384412acba251d87902ab928902f16.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45dddee525114c09ee0d1205aed6e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3b54e0dcdc081d45fb3df933cddc29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8257e16ded4d6fb13308f02fd460371.png)
您最近一年使用:0次
解题方法
5 . 在平面直角坐标系
中,已知
,点
满足以
为直径的圆与
轴相切.
(1)求
的轨迹
的方程;
(2)设直线
与
相切于点
,过
作
的垂线交
于
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2347bec7975dab2b8bce2fd19b1237d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9f9df9ac495aece618567662b77565.png)
您最近一年使用:0次
名校
6 . 已知函数
.
(1)求函数
在点
处的切线方程;
(2)若函数
只有一个极值点,求实数
的取值范围;
(3)若函数
(其中
)有两个极值点,分别为
,
,且
在区间
上恒成立,证明:不等式
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca47d2e8724200bf868215c66c5cfe40.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/903e63d4a34cc16c1f28b66298272889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d12d46d386c33dc0f9abcafb323c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db1b7b5e4953a249b88d2eec36364af.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/e2613fa3f3008e09c1204631b4b2c0d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694dc2a9102d1272d75be70a81bab75e.png)
您最近一年使用:0次
2020-01-12更新
|
505次组卷
|
4卷引用:福建省建瓯市芝华中学2023届高三上学期暑期考试数学试题
7 . 函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6a99faca87b50eb905f21c5fcdc8c4.png)
令
,
.
(1)求
并猜想
的表达式(不需要证明);
(2)
与
相切,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6a99faca87b50eb905f21c5fcdc8c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ef42799c2fa1e691a331b4d94fbc70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0e8e8f252eaa414599e70f147bad8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a4eff83c86011011a5e0e8b48ad5a8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c96bc7c7acf94b76def93c71dc156fb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3dd436444caca45aa03d5332ff84f0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b56692fcfc67a9cac9e2ce34138ec6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2019-07-12更新
|
252次组卷
|
2卷引用:福建省泉州市普通高中2018-2019学年高二下学期期末数学试题
名校
8 . 已知
是自然对数的底数,函数
与
的定义域都是
.
(1)求函数
在点
处的切线方程;
(2)求证:函数
只有一个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cfb32405d71542f1c87dd58d9d5c4a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7b896474b95cf035d59530216139da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0324fecb070287715e3e8f2322056922.png)
您最近一年使用:0次
2019-04-13更新
|
710次组卷
|
2卷引用:【全国百强校】福建省厦门市厦门外国语学校2019届高三最后一模数学(文)试题
9 . 设函数
,曲线
在点
处的切线
与直线
垂直.
(1)求
的解析式;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee64ce1df4ae1e5baaded5f24e1ab1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95f6ed76662695d4c711be57a16c3197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04836ba2906cf6f1e9aecd2a00824aae.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9393fc75283aabe25e4730e4aa04cad.png)
您最近一年使用:0次
11-12高一上·湖北·期末
名校
10 . 设函数
,其中
为自然对数的底数.
(1)当
时,判断函数
的单调性;
(2)若直线
是函数
的切线,求实数
的值;
(3)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/746f844aac17f3d79511d5984082f9dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49f28cbd784659e1d8d5a34c17466c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a2c484991fe4b01bd56c77a08a0e1da.png)
您最近一年使用:0次
2019-06-05更新
|
1450次组卷
|
10卷引用:2010-2011年福建省四地六校高二下学期第一次月考数学理卷
(已下线)2010-2011年福建省四地六校高二下学期第一次月考数学理卷(已下线)2011届福建省莆田十中高三5月月考调文科数学(已下线)2010-2011年湖北省沙市中学高一上学期期末考试数学理卷(已下线)2011届吉林省油田中学高三第一次模拟考试数学理卷(已下线)黑龙江省牡丹江一中10-11学年高二下学期期末考试数学(理)(已下线)2011-2012学年广东省揭阳一中高二下学期第一次阶段考试理科数学【市级联考】江苏省南通市2019届高三适应性考试数学试题2020届江苏省常州市高级中学高三上学期10月月考数学试题(已下线)2022年新高考北京数学高考真题变式题13-15题(已下线)2022年新高考北京数学高考真题变式题19-21题