名校
1 . 已知
在
处的切线方程为
.
(1)求实数
的值;
(2)证明:
仅有一个极值点
,且
.
(3)若
,是否存在
使得
恒成立,存在请求出
的取值范围,不存在请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5387267b6f5965456de8f0e0bdf964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58153bf3fdc83363cb5a23a2740d3778.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dec9c729c13d5db8e8929f726c3abcb.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cae1d9c7098a778798abc2e7b60151a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfaf5afd77bd894df1e1a672040de990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2 . 已知函数
,给出下列四个结论:
①当
时,对任意
,
有1个极值点;
②当
时,存在
,使得
存在极值点;
③当
时,对任意
,
有一个零点;
④当
时,存在
,使得
有3个零点.
其中所有正确结论的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105861d1641ea050b3274e1dac21c6fc.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a882037b9ce104ecc496e0f31a139361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c7b17b40ac22797b8d263c4eb19653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36b234ba460321e811de1729eadd4b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22fc53d1a6192701c1d7364c08fac090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36b234ba460321e811de1729eadd4b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
其中所有正确结论的序号是
您最近一年使用:0次
解题方法
3 . 已知函数
,给出下列四个结论:
①函数
是奇函数;
②
,且
,关于x的方程
恰有两个不相等的实数根;
③已知
是曲线
上任意一点,
,则
;
④设
为曲线
上一点,
为曲线
上一点.若
,则
.
其中所有正确结论的序号是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d08e4a96cfcea8a303b56b35cafb47fb.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b10c7c83af99e5686133623e29c455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23899cffeb0d20e29e7212a7327c604a.png)
③已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/482ad28bbcbe8b8d384d84851a54386b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f614a56621170153a1a1c582a145ba.png)
④设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/793894c733026e3f5900b31538fcb731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2dff006a89ed43e44492206e8516e7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3d36c7faa45fe5dae65a800cb59c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778083c63e464acd369abc5e667c8d74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f850a3ec66b1438ca4da2c30b6939ea9.png)
其中所有正确结论的序号是
您最近一年使用:0次
名校
4 . 设函数
,
.曲线
在点
处的切线方程为
.
(1)求a的值;
(2)求证:方程
仅有一个实根;
(3)对任意
,有
,求正数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c927a4fcfc5c875001648ac315ae17c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31c4f39399ec245a67db2933ed639f2.png)
(1)求a的值;
(2)求证:方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a73db674d29eae8f8921eff5944983.png)
(3)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44672d44c44a6bf67ec4243399b0e5.png)
您最近一年使用:0次
2024-04-22更新
|
1293次组卷
|
5卷引用:北京市顺义区2024届高三第二次质量监测数学试卷
解题方法
5 . 已知
是定义在
上的函数,其图象是一条连续不断的曲线,设函数
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac87434324956e4145e38ad92a1aa95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb92a5f4841d7675abb9d9500c14436.png)
A.若![]() ![]() ![]() ![]() ![]() |
B.对于任意实数![]() ![]() ![]() ![]() ![]() |
C.对于任意实数![]() ![]() ![]() ![]() ![]() |
D.若函数![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f5745682e5823ffaece03ff00945c6.png)
(1)求曲线
在点
处的切线方程;
(2)求证:
;
(3)若函数
在区间
上无零点,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f5745682e5823ffaece03ff00945c6.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89f5698f41b542aff4bcebbc81ff92b.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307eabe27b259f882d79a7eef5598492.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
您最近一年使用:0次
解题方法
7 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)若
是增函数,求a的取值范围;
(3)证明:
有最小值,且最小值小于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/792c57367bafbfcc9931b68ef0a23cf1.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.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/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74156327e5659301f391814605688899.png)
您最近一年使用:0次
2023-04-25更新
|
1199次组卷
|
3卷引用:北京市丰台区2023届高三二模数学试题
名校
解题方法
8 . 若函数
的极小值点为1,则实数a的取值范围是__________ ,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/309d02ea809ae727e69c7dc47819c00b.png)
您最近一年使用:0次
2023-02-22更新
|
1195次组卷
|
4卷引用:北京市清华大学THUSSAT2023届高三上学期12月诊断性测试数学(理)试题
名校
9 . 已知函数
.
(1)求曲线
在点
处的切线方程;
(2)求函数
的极值;
(3)当
时,设函数
,
,判断
的零点个数,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e20a21999ea818acdfb48d3641f70d3b.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3882fd82c321d981b049e52eba209ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b22149b97d51ea1171c46fadee5162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ffd1f6bd3686a07efa4086a02b96a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
10 . 如图,某荷塘里浮萍的面积y(单位:
)与时间t(单位:月)满足关系式:
(a为常数),记
(
).给出下列四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/bae00e48-adab-491e-aa9e-1f67099720cc.png?resizew=163)
①设
,则数列
是等比数列;
②存在唯一的实数
,使得
成立,其中
是
的导函数;
③常数
;
④记浮萍蔓延到
,
,
所经过的时间分别为
,
,
,则
.
其中所有正确结论的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c901bcdfa58f0c68ad0161b0bab269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e59e0f98f26ebe820762e0c1aefe9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4dafff83fd807d0010d1805d9f4552e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c81b29ac8a01886b25dcef55c5f6877.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/bae00e48-adab-491e-aa9e-1f67099720cc.png?resizew=163)
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/accfc1380a80460fb38bcc42362d093f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
②存在唯一的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2873e2f67c3d2ebf981711e043247981.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a973a64f8cf341c339c9ee9cd0706d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe918c6a811837af4db00ee457ac791c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2709ca478fb15ea08e8aa55328eae8e6.png)
③常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fae35542c8e8114f3cfc05b400ba565.png)
④记浮萍蔓延到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d282f2e8724f5a37a02c470aca736a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c3e2cd96b8a9873b302609af16b0bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddc7a20a7f8e8dc4b24a9ac6db2a5dba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c7eb49a823f757461cd5260757b088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd84a8f95166367063218ee03ffd5a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db31d2bbc9b044646fd026f239e7b62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a5cd1429905bb39094ca225f07c1740.png)
其中所有正确结论的序号是
您最近一年使用:0次
2022-04-27更新
|
1554次组卷
|
7卷引用:北京市丰台区2022届高三高考二模数学试题
北京市丰台区2022届高三高考二模数学试题(已下线)临考押题卷04-2022年高考数学临考押题卷(北京卷)北京市育英学校2023届高三上学期数学统测(一) 试题北京卷专题12导数及其应用(选择填空题)重庆市万州第二高级中学2021-2022学年高二下学期6月第四次质量检测数学试题(已下线)专题08 函数模型及其应用(针对训练)-2023年高考数学一轮复习精讲精练宝典(新高考专用)(已下线)第四章 导数与函数的零点 专题四 导数中隐零点问题 微点4 导数中隐零点问题综合训练