名校
解题方法
1 . 函数
,
有两个不同的极值点
,
,
(1)求实数a的取值范围;
(2)当
的取值范围为
时,总存在两组不同的数对
使得方程
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c986e3e976ad88324f486dcd2e811d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd888afdcfdb3e91a157d50f65e915e.png)
(1)求实数a的取值范围;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66142696737fa069287a4db771f799a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8aa7d09b1316af035dfa1865defc7d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f803a468e5d66004e57372a5bf2c5e1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972c9c30e2c87d549e73f945ff58150c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
解题方法
2 . 函数
,
有两个极值点
,
,
(1)求实数a的取值范围
(2)不等式
恒成立,试求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b81fd69f723fa766b54ff5ec7abf1e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd888afdcfdb3e91a157d50f65e915e.png)
(1)求实数a的取值范围
(2)不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/763b0f19b62f88c528f8bd6acaeac6d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
.
(1)
,求实数a的取值范围;
(2)
,使
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0d8306a1e7c274aec312312e5d29c4.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ae156029f0c6e11c0dab4dfdbdd2737.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5583be183d68cd21a5e5e512e3485630.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f987479ff1ee3c5248ccf060dc30f189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b11c4ba7cbaf63a123f4dd942434f291.png)
您最近一年使用:0次
名校
解题方法
4 . 已知
.
(1)若
恒有两个极值点
,
(
),求实数a的取值范围;
(2)在(1)的条件下,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307ed483bea9d2e58981551eb3720fb7.png)
(1)若
![](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/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
(2)在(1)的条件下,证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33870d20e5d61b8b37d9ecd8282fe257.png)
您最近一年使用:0次
2022-06-01更新
|
1095次组卷
|
5卷引用:黑龙江省哈尔滨市第三中学校2022届高三第五次高考模拟考试理科数学试卷
黑龙江省哈尔滨市第三中学校2022届高三第五次高考模拟考试理科数学试卷(已下线)第12节 导数的综合应用(已下线)专题11 导数及其应用难点突破3-利用导数解决双变量问题-1黑龙江省佳木斯市第十二中学2021-2022学年高二下学期期末考试数学试题陕西省商洛市洛南县第二高级中学2022-2023学年高三上学期三模理科数学试题
解题方法
5 . 已知函数
,
.
(1)求证:
,
;
(2)若存在
、
,且当
时,使得
成立,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf8c74ed29417953a949b06dd4ad44cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d49ec515fb1fdc93ca4dda443326ad5.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe6dd16202517a535f2730f2da7fa12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d49ec515fb1fdc93ca4dda443326ad5.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/646c95700c1202ff8c0d21dfa09358a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859458471c86ae39e0cc42d2d960d03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb9c68fd0d28795c4a9fe6a9ce8cd8e0.png)
您最近一年使用:0次
解题方法
6 . 已知函数
的最小值为1.
(1)求实数
的值;
(2)过点
作
图象的两条切线MA,MB,A(
),B(
)是两个切点,证明:
>1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082ece762ffbf92921f4685d45f5166d.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f85bdfbba6ab48ab99b16453ee5025b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf2102b730fe50c8681f1a6fafe67af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c788875fe76212a7c59d0a9cee345d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ceddc345bfa05b7c0c61ec02470188a.png)
您最近一年使用:0次
2022-05-22更新
|
740次组卷
|
4卷引用:2022届普通高等学校全国统一模拟招生考试(新未来5月联考)文科数学试卷(全国乙卷)
2022·全国·模拟预测
7 . 已知函数
(其中
为自然对数的底数).
(1)讨论函数
的单调性;
(2)若
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09127574eb8200816b886328f7c4056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd97e253b345a0a9864f1dac91de314.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec72ca557aa4229ee871628ffcf0d8a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33eba741c09947fb09136ff9af42608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2022·全国·模拟预测
8 . 已知函数
.
(1)当
时,求曲线
在
处的切线方程;
(2)若
存在两个极值点
、
,求实数
的取值范围,并证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd66abc949fe3e0a87c9c7c2ea2dfeca.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040135d64192de075ba0cc9f11ddbc9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa33c2bd791339d32821077846605d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23511c94672f1eb1ad2355c3bbc303c.png)
您最近一年使用:0次
解题方法
9 . 设
为实数,函数
.
(1)判断函数
在定义域上的单调性;
(2)若方程
有两个实数根
,证明:
(
是自然对数的底数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41228bf95cbbe36b67306e140f8d19c6.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51b342e17fe59d653f89a82c3389a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69f02b52c7928235fe5e25b4c5ca4ebc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797bbd18359c9a29842b39109b3a0aac.png)
您最近一年使用:0次
名校
解题方法
10 . 已知
是函数
的一条切线,
,且
是
的导数.
(1)求
的值;
(2)证明:当
,
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb70fdf064b9193e506ca43f4672af56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a982990e6a65123ec91baba94168ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b1c10ac0d5434396a941a27c5cf668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51350a90203fcdc2d500a89061b7f52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f02d1c039d9420ce3f9b3e9d58ab08d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bb5ac10a2ab38b9f4c31a318422a4c.png)
您最近一年使用:0次
2022-05-12更新
|
590次组卷
|
3卷引用:福建省厦门第一中学2021-2022学年高二下学期期中考试数学试题
福建省厦门第一中学2021-2022学年高二下学期期中考试数学试题(已下线)期末押题预测卷01(考试范围:选修二+选修三)-2021-2022学年高二数学下学期期末必考题型归纳及过关测试(人教A版2019)广东省潮州市饶平县第二中学2021-2022学年高二下学期月考(二)数学试题