名校
1 . 已知
.
(1)求函数
的单调区间和极值;
(2)请严格证明曲线
有唯一交点;
(3)对于常数
,若直线
和曲线
共有三个不同交点
,其中
,求证:
成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647014ad8af603468f4100043c4bde15.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/720777756eaef6fd797e16c7656bd916.png)
(2)请严格证明曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/720777756eaef6fd797e16c7656bd916.png)
(3)对于常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3387f1c69de6c2407212536b35150e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46111e4d12c21798aa213c0d7804c2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/720777756eaef6fd797e16c7656bd916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3059524807d8e93433b8d994df6ede70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7169ce3255d2a02a20aa5932d2bd48.png)
您最近一年使用:0次
2023-12-19更新
|
636次组卷
|
3卷引用:上海市嘉定区2024届高三一模数学试题
名校
解题方法
2 . 记集合
,集合
,若
,则称直线
为函数
在
上的“最佳上界线”;若
,则称直线
为函数
在
上的“最佳下界线”.
(1)已知函数
,
.若
,求
的值;
(2)已知
.
(ⅰ)证明:直线
是曲线
的一条切线的充要条件是直线
是函数
在
上的“最佳下界线”;
(ⅱ)若
,直接写出集合
中元素的个数(无需证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8ed79e83f9896873e80c3c4b5a935d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0bf53ee2722352957ab61f90a49daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54ade3f669537d031a2be1b4f24a626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f4d45f004ca5fbf9a9bb4f0eef8232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165beb63772ec0f7797a71646d0a1ebc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f4d45f004ca5fbf9a9bb4f0eef8232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7cc26a0fe4103db9229df034d5aa70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf2f55da363aa19912ee465d3eb2737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063bb2a5c220db357fa36417de213ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da66a74e8ab43f08d4b3949bb7d24e4.png)
(ⅰ)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f4d45f004ca5fbf9a9bb4f0eef8232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f4d45f004ca5fbf9a9bb4f0eef8232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac87434324956e4145e38ad92a1aa95.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a669064772daefdeb12c3ebaf01a581f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a494f5a36475e96c7bc69589f70c3a86.png)
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2024-05-07更新
|
474次组卷
|
2卷引用:福建省福州市2023-2024学年高三下学期4月末质量检测数学试卷
3 . 已知函数
(
).
(1)讨论
的单调性;
(2)设
,若函数
有两个不同的极值点
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dca377668811d6b06bcacda9228c040.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98bafb84cd3f290d9c5920db47ff1180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59b4ae053a3f1e3d3ac7afaa9aac77b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac59ef367ebf2e36b984c2f6fd913e9.png)
您最近一年使用:0次
名校
4 . 已知函数
.
(1)当
时,求
的单调区间;
(2)若
时,
,求a的取值范围;
(3)对于任意
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27862c9517dbb4eb17a6725eb142969.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(3)对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1af027bd16e380d3be03a9761ca56055.png)
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2024-01-18更新
|
2007次组卷
|
9卷引用:山东省济南市2024届高三上学期期末学习质量检测数学试题
5 . 已知函数
.
(1)求函数
的单调区间;
(2)若
,且
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891c3b61504044e5f1f675c0eb3dc7ac.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41bc57877dc371372dc4145d2b56f6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c960fc862fd36db83082f5c50cd604b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ec30573e9ef491771f219d4b2c22f78.png)
您最近一年使用:0次
名校
6 . 设函数
,其中
为实数.
(1)当
时,求
的单调区间;
(2)若函数
在定义域内有两个不同的极值点,求
的取值范围;
(3)设
的两个不同的极值点为
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5623411fa3819127f6fe67d93e77dcda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](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/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa4790fbf12830c009aa2c0d4dd3a8f.png)
您最近一年使用:0次
7 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18592f513d46d69927f86d1c03e0753e.png)
(1)当
时,求
的单调区间;
(2)已知
,求证:当
时,
恒成立;
(3)设
,求证:当函数
恰有一个零点时,该零点一定不是函数
的极值点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18592f513d46d69927f86d1c03e0753e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d191d6de821fbb06a51b5a20112db6de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b666663ce3537a634a3b427b418eb62.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860eac9c5a33894ff90b68457dd17b30.png)
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名校
8 . 已知函数
.
(1)若
,求
的单调区间;
(2)若
时
恒成立,求实数a的取值范围.
(3)定义函数
,对于数列
,若
,则称
为函数
的“生成数列”,
为函数
的一个“源数列”.
①已知
为函数
的“源数列”,求证:对任意正整数
,均有
;
②已知
为函数
的“生成数列”,
为函数
的“源数列”,
与
的公共项按从小到大的顺序构成数列
,试问在数列
中是否存在连续三项构成等比数列?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3374eaf3f06eeb1ac4272d402cfa1b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcac1e85463a3177f487d896b3d1d24c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
(3)定义函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0914c295f572c98dd043d4f84268934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b9599b8c0f6a10d15f408ad651b35c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
①已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72878dfe2c7a76d76287194ac4bdf4ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729b4033af5b0c9c4889406d2c8294f7.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a386e4d3f92631ed64ca3e2f5f4725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
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2023-12-25更新
|
718次组卷
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4卷引用:上海市静安区回民中学2024届高三上学期12月阶段性测试数学试题
上海市静安区回民中学2024届高三上学期12月阶段性测试数学试题湖南省邵阳市第二中学2024届高三下学期入学测试数学试题(已下线)第五章 导数及其应用(单元重点综合测试)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)上海市浦东复旦附中分校2023-2024学年高三下学期3月月考数学试题
9 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ed07b0ce942687ba7a87c997a7b767.png)
(1)讨论函数
的单调性;
(2)若
,证明:
,
.(提示:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ed07b0ce942687ba7a87c997a7b767.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc55062abcda348cb4cf9837e2ab936d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bad5c8a4e4bad474651c0a61de820ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aaa7db4b6344ee1bc22e47e4c760533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abe8be09d4ab0e414d110e09ee20e3df.png)
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2023-10-12更新
|
154次组卷
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2卷引用:辽宁省朝阳市名校联考2023-2024学年高三上学期开学数学试题
名校
解题方法
10 . 已知:函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ad23c0ef2d67af4844df5175b41ff1.png)
(1)求
的单调区间和极值;
(2)证明:
;(参考数据:
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0891a54fcf7ccbd9e6b8680944bc580d.png)
(3)若不等式
的解集中恰有三个整数解,求实数
的取值范围.(三问直接写出答案,不需要详细解答,参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ad23c0ef2d67af4844df5175b41ff1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd2cd53f618f890b0711f833ecff7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a80d0cbe26bbac441eceb3e71a29010e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0891a54fcf7ccbd9e6b8680944bc580d.png)
(3)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f0eb2dcdd8c486c0f3e0856e2e02a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7722e21105bd9b5610506279805ba53c.png)
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