名校
解题方法
1 . 若函数
在
上有定义,且对于任意不同的
,都有
,则称
为
上的“
类函数”.
(1)若
,判断
是否为
上的“2类函数”;
(2)若
,为
上的“2类函数”,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f0e1ac411fd3a260a5c71df178bd7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b62f64bce0222f01a519ab1b26236bcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca6d68f1de3e70696f1d5d60affe6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee4613910bb8aa030db2fc5d2768e533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f248318141e0016d38f9f5a692797f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a3616e4a7268ef41b750fe22afbcd74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f248318141e0016d38f9f5a692797f.png)
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2024-05-08更新
|
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3卷引用:辽宁省沈阳市东北育才学校2023-2024学年高二实验部下学期阶段检测二(6月)数学试题
名校
2 . 已知函数
.
(1)讨论
的单调性;
(2)若
有
个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd46df10da04a7be0fb3873b8aca8be.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-05-08更新
|
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3卷引用:辽宁省本溪市县级重点高中协作体2023-2024学年高二下学期期中考试数学试卷
3 . 若过点
可以作曲线
的两条切线,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3af21071d48088a22d33bca27c93557f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8190660962c1d992d7d61a69c21a2737.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7卷引用:辽宁省本溪市县级重点高中协作体2023-2024学年高二下学期期中考试数学试卷
辽宁省本溪市县级重点高中协作体2023-2024学年高二下学期期中考试数学试卷广东省顺德区北滘中学2023-2024学年高二下学期期中考试数学试卷(已下线)易错点3 曲线上的点与切点辨别不清广东省汕头市金南实验学校2024届高三下学期三模数学试题广东省佛山市桂城中学2023-2024学年高二下学期第二次段考数学试卷(已下线)专题08 导数的运算、几何意义及极值最值常考题型归类--高二期末考点大串讲(人教B版2019选择性必修第三册)(已下线)导数及其应用-综合测试卷B卷
名校
解题方法
4 . 已知函数
.
(1)若曲线
在
处的切线方程为
,求实数
的值;
(2)若对于任意
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eedd86fef4f51338807333d879255e6f.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95fb8b61d7fa8ecd5ea45762c7400e6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f48697046ef1531aaaf9e18cfb27254.png)
(2)若对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8252d311939755d058364be076ec1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2卷引用:2024届辽宁省高考扣题卷(二)数学试题
名校
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb10f8ecb4ec7d3136bc662867968f2.png)
(1)若
求曲线
在点
处的切线方程.
(2)若
证明:
在
上单调递增.
(3)当
时,
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb10f8ecb4ec7d3136bc662867968f2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20439836def79ea69d967d95e81320a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87676cc3ca413d9ba64fab2cd45c909c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ec994bb92d9945a4369f1215d859ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-05-08更新
|
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4卷引用:辽宁省本溪市县级重点高中协作体2023-2024学年高二下学期期中考试数学试卷
名校
解题方法
6 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1864b98153200f5929787295de2c1e38.png)
(1)求
的最小值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/001add838968419287e3f16eb55c00b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1864b98153200f5929787295de2c1e38.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08cf938e64d3b789ea0ba38177a275cc.png)
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7 . 已知函数
.
(1)讨论函数
的单调性;
(2)当
时,数列
满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6aa8089b5d9b722aff679af3c4d289.png)
①求证:
;
②求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0730ea5a5d9d25f1c012a78b390e8bc4.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6aa8089b5d9b722aff679af3c4d289.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c101acd1f4d2d79055068877921c2b5d.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/984992c5bb21f9ac5bdaad6c228f2e25.png)
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解题方法
8 . 已知
.
(1)讨论函数
的单调性;
(2)当
时,证明:函数
有且仅有两个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7222eb00539edf2ac3fc201866eb1d5d.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a415767156945ea8ada9ed3756019fc.png)
您最近一年使用:0次
名校
9 . 设函数
.
(1)讨论
的单调性.
(2)证明:
.
(3)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/181d3aa3dec00a9c63fa2987c77bd0ea.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c1e0c67c135532494ef7cf732fb7ef.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d4a677b734a48f8116d67afceead44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95ca867dde8e6812ba191138994b13.png)
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10 . 已知函数
.
(1)求曲线
的平行于x轴的切线的切点横坐标;
(2)证明曲线
与x轴恰有两个交点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48c89e5976bcde936dc841b1bc8ab80.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)证明曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
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