名校
1 . 已知函数
,
.
(1)求函数
的最小值;
(2)过点
的直线
与交
于A、B两点,求证:
为定值;
(3)求证:有且只有两条直线与函数
的图像都相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590eeefa9b43063edc41ac94f5e02956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5215c31948a7413fc23f5d9ed2ec92.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8461a90d113f79f265e2f364ce419808.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836e8ad6a92a4c3334bf2ccd7147dc32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bece4bb3068ac3b5f9c875f1111c24.png)
(3)求证:有且只有两条直线与函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
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解题方法
2 . 已知函数
.
(1)若
是定义域上的严格增函数,求a的取值范围;
(2)若
,
,求实数a的取值范围;
(3)设
、
是函数
的两个极值点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88989bd25633343872906735f419f1c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(3)设
![](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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a9ebdef373d79fa9774db3a885205ea.png)
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解题方法
3 . 已知
.
(1)求函数
的极小值;
(2)当
时,求证:
;
(3)设
,记函数
在区间
上的最大值为
,当
最小时,求a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21b470f563042f1477f615819d547666.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71caec84a4be2c3d7f14f5e25bca4d53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a027ca3feaa4b2ba76a43709004998.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9944840b010bd79a95adec8380f90697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b26c416363ab2a9ed000b429540db55e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760f804646698060703c5458ff5637c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760f804646698060703c5458ff5637c7.png)
您最近一年使用:0次
2023-06-02更新
|
481次组卷
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2卷引用:上海市复兴高级中学2023届高三适应性练习数学试题
4 . 已知
.
(1)当
时,求函数
的单调减区间;
(2)当
时,曲线
在相异的两点
点处的切线分别为
和
和
的交点位于直线
上,证明:
两点的横坐标之和小于4;
(3)当
时,如果对于任意
,总存在以
为三边长的三角形,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50a5b1b35f29dfec58eb44bcc9a89f2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac9eb4f13a6ec140f7050e8d7dde52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c7d2c85e7878b6cbfb45b71ffb60b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5631bc68728bbf17b87c3e7e7f8e425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bc82aed391363566b80c93ddfab5111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
5 . 已知函数
.
(1)
,求实数
的值;
(2)若
,且不等式
对任意
恒成立,求
的取值范围;
(3)设
,试利用结论
,证明:若
,其中
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0d64a2ac63c7dcdcca10435424fd64.png)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8190514daf055718b344deb8d89d9b4f.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e5b4d7acd5a634c39e7ce15438af35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0d7fbcc396c7b646c31f60e32d9e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ab8f56a3c83c8f15cde2b18ecfe4c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9322dd8f56b5f8d2c667fdf0d4a9f9aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9098338d53471dd9041390613b25171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f82861c837fa4532cbac67fffb92751.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157e56f61c39d6367a6e15715d81e18f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0d64a2ac63c7dcdcca10435424fd64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994cbe1941c51dbe4faba0aaa3a9d41d.png)
您最近一年使用:0次
2023-05-30更新
|
589次组卷
|
3卷引用:上海市七宝中学2023届高三三模数学试题
名校
解题方法
6 . 已知函数
.
(1)求证:
;
(2)若
,试比较
与
的大小;
(3)若
,问
是否恒成立?若恒成立,求
的取值范围; 若不恒成立,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc7a277581319a8a8257ab3ce84cf0b.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257e0a13428a004a923b59d092cf77de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22165fb1166b885fec563eb95b778882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f01e03edfbc7ad3ffd890fd0e682458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-05-30更新
|
662次组卷
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2卷引用:上海市曹杨第二中学2023届高三5月模拟2数学试题
名校
解题方法
7 . 已知函数
,其导函数为
,
(1)若函数
有三个零点
,且
,试比较
与
的大小.
(2)若
,试判断
在区间
上是否存在极值点,并说明理由.
(3)在(1)的条件下,对任意的
,总存在
使得
成立,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6092b74ceb6b5f63578d9c6af2bde50b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7169ce3255d2a02a20aa5932d2bd48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6735266eae37b634bb62f0318d03e3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1886d4011bc0befe41a4c9ed8c796a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146dcc23e6649b974b70861a26de0488.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02d6f434da3988371050909c9201c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094cba781181aeb90752170e9ba6c94.png)
(3)在(1)的条件下,对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7569cd7e9b31ad838230133b9bc8314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3606fd3966dc72e0f8a32047945a86e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078bae9e06b9cb047c8837828db6ec23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2023-05-29更新
|
754次组卷
|
3卷引用:上海市七宝中学2023届高三5月第一次模拟练习数学试题
上海市七宝中学2023届高三5月第一次模拟练习数学试题上海市嘉定区第二中学2023届高三三模数学试题(已下线)第七章 导数与不等式能成立(有解)问题 专题四 双变量能成立(有解)问题的解法 微点3 双变量双函数能成立(有解)问题的解法(二)
8 . 若函数
满足
,称
为
的不动点.
(1)求函数
的不动点;
(2)设
.求证:
恰有一个不动点;
(3)证明:函数
有唯一不动点的充分非必要条件是函数
有唯一不动点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/359baaa1ce86fe2403796f44d62429fb.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb0d493ff8d41fbcb33ad51365f46a23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8166c6ec3cfe1f17dabc7b307cb2e1a.png)
(3)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276b142a9d9f0a87425a668dd6501f15.png)
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解题方法
9 . 设
是定义在区间
上的函数,其导函数为
.如果存在实数
和函数
,其中
对任意的
都有
,使得
,则称函数
具有性质
.
(1)设函数
,其中
为实数.
(ⅰ)判断函数
是否具有性质
,请说明理由;
(ⅱ)求函数
的单调区间.
(2)已知函数
具有性质
.给定
,
,设
为实数,
,
,且
,
,若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cc2395f479a7f620dc7a8168f87adef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2c2e62820db54ca0d6c40aa6fadef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbde2170c24819edd47db617810bf47.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f7b185e766962ce57d97360e82f54e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(ⅰ)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/904f7b7f1d38d1ca3d3e60241ec07abd.png)
(ⅱ)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5d8bc28ee110a9540f383828b7d245.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c68882f2800fded4fb29e05d1bf1f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/513cd118822a9636e0d04af9afe980f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e3f36a6f424089eb52f263c41bb48c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b68031c3405c23f82fb3f352e44a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea1deca2850e28ae2578f503c277a7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/775bf5cae131754ffe414799a55ff91b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
10 . 定义:若曲线C1和曲线C2有公共点P,且在P处的切线相同,则称C1与C2在点P处相切.
(1)设
.若曲线
与曲线
在点P处相切,求m的值;
(2)设
,若圆M:
与曲线
在点Q(Q在第一象限)处相切,求b的最小值;
(3)若函数
是定义在R上的连续可导函数,导函数为
,且满足
和
都恒成立.是否存在点P,使得曲线
和曲线y=1在点P处相切?证明你的结论.
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e3eea6e9e68deb9799e4492f596c48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c13ca144c2fe2e7a2a42cb25785ec4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b466f39f2a89f9acc35986098b1a31b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a401146416b25488b8b21501e5d9ab4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda01771ec500241e3b99d0b63ea3a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf2dd9defca825ed67709b3b67d2b4e.png)
您最近一年使用:0次
2023-05-28更新
|
559次组卷
|
4卷引用:上海市奉贤中学2023届高三三模数学试题
上海市奉贤中学2023届高三三模数学试题(已下线)上海市华东师范大学第二附属中学2022-2023学年高二下学期期末数学试题上海市上海中学东校2023-2024学年高二下学期5月月考数学试卷(已下线)上海市高二下学期期末真题必刷04(压轴题)--高二期末考点大串讲(沪教版2020选修)