名校
1 . 已知函数
.
(1)讨论函数
的单调区间;
(2)当
时,函数
有两个零点
,求
的取值范围:
(3)在(2)的条件下,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/784548dbfa097ef19fd7a4e68739e478.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e189dbc979fad6bf8ca03ac1388cbac0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff60eab72de85437e12806474281612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)在(2)的条件下,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc93e6c831bd03403d423b88746e733.png)
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2024-04-01更新
|
344次组卷
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3卷引用:江苏省新海高级中学2023-2024学年高二下学期阶段性测试(一)数学试题
名校
2 . 已知函数
.
(1)若
在区间
上有极值,求实数
的取值范围;
(2)当
时,求证:
有两个零点
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e72084f148e60046b29190a4bd1a396.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f114df5ceabdb7e5fd3fdad4eaf056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](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/26f3560f0c5eedffa5ce38fde2db28c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87ed5748e555b5ccb929aeabd6c7cd6.png)
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2023-11-07更新
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595次组卷
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3卷引用:江苏省连云港市灌云高级中学2024届高三上学期第一次月考数学试题
江苏省连云港市灌云高级中学2024届高三上学期第一次月考数学试题江苏省苏州市2023-2024学年高三上学期期中数学试题(已下线)专题04 导数及其应用(4大易错点分析+解题模板+举一反三+易错题通关)
3 . 已知函数
,若对任意
,
,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddc07516ce0d7a67c958286a69ee99e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e842a695fe72b2ca98c6b0c503b34f96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff693f1f613c0304be5b1f5f281761bc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-10-13更新
|
716次组卷
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3卷引用:江苏省连云港市2023-2024学年高三上学期教学质量调研(一)数学试题
江苏省连云港市2023-2024学年高三上学期教学质量调研(一)数学试题(已下线)江苏省南通市如皋市2023-2024学年高三上学期教学质量调研(一)数学试题安徽省卓越县中联盟2024届高三上学期第三次质量检测数学试题
名校
解题方法
5 . 已知函数
,且
,
.
(1)若
,函数
在区间
上单调递增,求实数b的取值范围;
(2)证明:对于任意实数
,
.参考数据:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b59588989187799f35748467128140ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76d4494d28279a01a2e2834cd272dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d8742c296a7949b598114a34c51f69.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1279ef84071f5ad7c4c1681357edd84.png)
(2)证明:对于任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19dc91cec629f47c4b325df10f8365a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7799d3f7e3bcfe780bdfab5faa4e43.png)
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2022-11-10更新
|
717次组卷
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2卷引用:江苏省连云港市灌云高级中学2024届高三上学期期末数学试题
6 . 已知函数
和
,它们的图像分别为曲线
和
.
(1)求函数
的单调区间;
(2)证明:曲线
和
有唯一交点;
(3)设直线
与两条曲线
共有三个不同交点,并且从左到右的三个交点的横坐标依次为
,求证:
成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86161d12df385eb4cfec8a8a38277fc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8da208132c56cf53ce7f4d0985582c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46111e4d12c21798aa213c0d7804c2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e632de0a4a7142242b1c4310b0a6f185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
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2022-12-26更新
|
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3卷引用:江苏省连云港市灌南高级中学2024届高三上学期期中数学试题
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7 . 已知函数
及其导函数
的定义域均为
,若
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d88f7a780da11dc796d1a638f71dd49a.png)
A.![]() |
B.![]() |
C.方程![]() |
D.![]() ![]() |
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2022-12-16更新
|
1909次组卷
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6卷引用:江苏省连云港市灌云高级中学2024届高三上学期11月月考数学试题
8 . 设函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff559aff18af00f4a58e9806e6b7202.png)
(1)讨论函数
的单调性;
(2)若
(其中
),证明:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5783ecf9d3196868fa33b6a769666189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff559aff18af00f4a58e9806e6b7202.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ba1babb8ef90a53bd3b36dbc55cb69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c534f574156e120f4a8d9ebef47ede.png)
您最近一年使用:0次
名校
9 . 已知
和
分别是函数
的两个极值点,且
,则实数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971905ea129aec0ca7c325f60260c7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd86badb20015aa65328fda1e43a117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2849c745af89b34fb00fc38ca0ea6bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32a86d65aab881fdd06a05ce47d09c6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-11-26更新
|
1257次组卷
|
5卷引用:江苏省连云港市灌云高级中学2024届高三上学期12月月考数学试题
解题方法
10 . 已知函数
其中
是自然对数的底数,
为正数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(1)若
在
处取得极值,且
是
的一个零点,求
的值;
(2)若
,求
在区间
上的最大值;
(3)设函数
在区间
上是减函数,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07829b9e293306ad862197c6839d5ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46ad5cbb3648233e44c795596540971e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/915f5f271326f69b6ee324b128eff816.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27ce93b9f0ea8d7e3a5e4a4f2fcacf45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe5239e374894f95da60c5cb35a2a718.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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