1 . 已知函数
在
处的切线在
轴上的截距为
.
(1)求
的值;
(2)若
有且仅有两个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2883815c0ffc16f8809913897e05f1c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d06e33d079ac1649ee5eea8f61de7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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2024-04-22更新
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4卷引用:福建省竺数教研2023-2024学年高三下学期质量监测数学试题
福建省竺数教研2023-2024学年高三下学期质量监测数学试题(已下线)模块一 专题5 《导数在研究函数极值和最值中的应用》A基础卷(高二人教B版)(已下线)广东省清远市2023-2024学年高二下学期期中联合考试数学试题变式题16-19山东省烟台市莱州市第一中学2023-2024学年高二下学期第四次质量检测数学试题
2 . 对于函数
,若实数
满足
,则称
为
的不动点.已知
,且
的不动点的集合为
.以
和
分别表示集合
中的最小元素和最大元素.
(1)若
,求
的元素个数及
;
(2)当
恰有一个元素时,
的取值集合记为
.
(i)求
;
(ii)若
,数列
满足
,
,集合
,
.求证:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73bc955d158efde0bdd62d14a60a65e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4687da5aca206a4974ecbac6901e40aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d51777d3fca1ee8f588a6c39190dae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698f45c9ed5bb04924f1037107e76988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74dec63e6d30a41fcc8972397875bf46.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc825a1d8739d18c7f2fcc0d489d4f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69742762f22dbde311d3cf86ffb00a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/556c5ed8c16b568bdf3c674e57131770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12d0bd9afdd4e53ff37f5bfcaa1106c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49377a64a56c87bb4fb916f9ae427c1e.png)
您最近一年使用:0次
名校
3 . 已知函数
.
(1)讨论
的单调性;
(2)若不等式
恒成立,求
的取值范围;
(3)当
时,试判断函数
的零点个数,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca503660e161b422720a08a53c3af343.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f4f4efb776c41d4190aa1c08572905e.png)
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2024-03-12更新
|
1288次组卷
|
3卷引用:福建省漳州市2024届高三毕业班第三次质量检测数学试题
名校
4 . 已知函数
.
(1)证明:当
时,
;
(2)若函数
有两个零点
.
①求
的取值范围;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12adf5ef80e4a31decd3e8ec1905a534.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b4f444d4dc94ff61b2e64e5ff92372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12bb063fcb1954df530b1d406f82305a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6d418c37e725323e7333bc26ff0526.png)
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2024-03-12更新
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2卷引用:福建省莆田市2024届高三毕业班第二次教学质量检测数学试卷
名校
解题方法
5 . 已知函数
有两个不同的零点,分别记为
,
,且
.
(1)求实数
的取值范围;
(2)若不等式
恒成立(e为自然对数的底数),求正数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e178299be0b5d8ebfe23963dc03d0521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186d93ba36fde8219cd40ce9c0d7f531.png)
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名校
解题方法
6 . 已知函数
.
(1)证明:对任意的
,都有
.
(2)若关于
的方程
有两个不等实根
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f991208bb21eb52f9bab02d90dd64b0d.png)
(1)证明:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047056c99b39c70fa40d3c8178e5b631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43920f5171ed31db2520ef00e4c5fc24.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb2e46f49adba6036e2624639a1b966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b677fee269b63c8ae43f0f6ddb5c70.png)
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7 . 已知函数
,其中
.
(1)讨论函数
的单调性;
(2)若
,证明:函数
有唯一的零点;
(3)若
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bca0c0fd7170d190e3e742db0e89033.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
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2024-02-18更新
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893次组卷
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3卷引用:福建百校联考2024届高三下学期正月开学考试数学试题
名校
8 . 若过点
可以作曲线
的两条切线,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/190b9ce555e91dc891a3e80fc776fd1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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9 . 已知函数
有两个不同的零点
,
.
(1)求实数
的取值范围;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd78eb2c0004a61bb5f8811e514162ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54cc18f9bf8ff3a5ffc779edaed73730.png)
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10 . 函数
,函数
若函数
恰有2个零点,则实数a的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1b9b3f6d704232c6920c368e33b9ae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13381f2109fad6335d2a738bc8b4daf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ec7987f88ec5e973e7771fefcc5e3e5.png)
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2024-01-22更新
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6卷引用:福建省莆田市莆田第一中学2024届高三上学期第一次调研数学试题
福建省莆田市莆田第一中学2024届高三上学期第一次调研数学试题天津市八校联考2023-2024学年高三上学期期末质量调查数学试卷(已下线)第二讲:方程与函数思想【练】(已下线)信息必刷卷01(天津专用)(已下线)模型9 分段函数含参的零点模型(高中数学大模型)(已下线)高二下学期第一次月考填空题压轴题十四大题型专练-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第三册)