1 . 已知函数
(
).
(1)试讨论函数
的单调性;
(2)若函数
有两个零点
,
(
),求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4c6c3e924b696f267db638da3ba7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)试讨论函数
![](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/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677124ed07918174f894273c8ae72ae6.png)
您最近一年使用:0次
名校
2 . 已知函数
.
(1)求曲线
在点
处的切线方程;
(2)若函数
在
上的最大值在区间
内,求整数m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1fd994df940d5e72e1ffb5af064c18.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01db9cbf6f3078a185951b272af6cc34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da5b8e19e0aaf01b401e4f239b3d9a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88ea43f1e36cc084b861b7f5ea0c12.png)
您最近一年使用:0次
2023-02-26更新
|
882次组卷
|
7卷引用:河南省名师联盟2023届高三下学期2月质量检测(联考)文科数学试题
河南省名师联盟2023届高三下学期2月质量检测(联考)文科数学试题四川省盐亭中学2023届高三第六次高考模拟检测数学文科试题陕西省榆林市绥德中学2023届高三下学期2月月考文科数学试题四川省绵阳中学2023届高三适应性考试(二)理科数学试题九师联盟河北省2023届高三下学期2月联考文科数学试题(已下线)模块三 大招9 函数零点问题的处理大招(已下线)重难点突破08 利用导数解决一类整数问题(四大题型)
3 . 已知
,
.
(1)讨论
的单调性;
(2)若
,
,试讨论
在
内的零点个数.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422d30a743e408c4712d9cdf96ae2459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a003543fa5824e2a0a7a406e64c6d045.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164e752e2711294fdaa037aac4620b34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca4be345087f993a4078e16c16608e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083479b94380e8d659eff92d10a1989d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7010397d58ddc41effcbd9bbd4d19cda.png)
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4 . 若有且仅有一条直线与曲线
和
都相切,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e35b9f4c6a8ad43e30a5834b0fd3705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 已知函数
.
(1)求函数
的极值点;
(2)当
时,当函数
恰有三个不同的零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4f91c758604d10516c5c1c9ec99ce27.png)
(1)求函数
![](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/cffa662f0273f0921c1fa4727f632395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
6 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad8ecc7e64cc90083e80614127211553.png)
(1)若a=1,b=2,试分析
和
的单调性与极值;
(2)当a=b=1时,
、
的零点分别为
,
;
,
,从下面两个条件中任选一个证明.(若全选则按照第一个给分)
求证:①
;
②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41c7aa4d7660f30035105946a7f71e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad8ecc7e64cc90083e80614127211553.png)
(1)若a=1,b=2,试分析
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)当a=b=1时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
求证:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83f2979dc3f3a6323ccafbaf1bcd045a.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65aab1a727c92794d5171114a415f93.png)
您最近一年使用:0次
7 . 椭圆曲线加密算法运用于区块链.
椭圆曲线
.
关于x轴的对称点记为
.C在点
处的切线是指曲线
在点P处的切线.定义“
”运算满足:①若
,且直线PQ与C有第三个交点R,则
;②若
,且PQ为C的切线,切点为P,则
;③若
,规定
,且
.
(1)当
时,讨论函数
零点的个数;
(2)已知“
”运算满足交换律、结合律,若
,且PQ为C的切线,切点为P,证明:
;
(3)已知
,且直线PQ与C有第三个交点,求
的坐标.
参考公式:
椭圆曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9656273cea815e9c38f5b423a786df95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3b61b75052082d32b4f395ec629d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff3a05fcf57fccf4289fadb439a155f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02ec372ff211f6b93ad213f67eed57b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace8e8a2a533a8c62386aaad29fcba06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e0ee254499b8d5f8a09dead12204492.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5473b8307312b1275ae3e206114349a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e0ee254499b8d5f8a09dead12204492.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ad8402e9295f4a4cde8b1a508152798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3b61b75052082d32b4f395ec629d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70780e53aab31d009faeaf1c8a3564a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7efe1b189db965f857c27c88414715e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f93a7d10e5e86606daa686fb5cb950d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fc232553cfd6222d857896bfd5a7750.png)
(2)已知“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e0ee254499b8d5f8a09dead12204492.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9849a648fcdeb7aefe903aaf852977b0.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d3522a66a525ab0d7ff4d3fa6b2cfa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683260f27f7fb8f91c1782153621806f.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdfaadcff67f1ac61b3e3b2b3cacbf32.png)
您最近一年使用:0次
2023-02-23更新
|
5353次组卷
|
15卷引用:2023年安徽省、云南省、吉林省、黑龙江省联考数学试卷评价
2023年安徽省、云南省、吉林省、黑龙江省联考数学试卷评价(已下线)2023年四省联考变试题17-22山西省大同市2023届高三阶段性模拟(2月联考)数学试题(A卷)(已下线)专题19新文化与创新试题(已下线)专题05导数及其应用(解答题)山西省大同市第一中学校等2校2023届高三一模理科数学试题(已下线)专题15 圆锥曲线综合(已下线)函数的图象与性质(已下线)新题型01 新高考新结构二十一大考点汇总-3(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大题型)(练习)(已下线)专题8 考前押题大猜想36-402023届安徽省、云南省、吉林省、黑龙江省高三下学期2月适应性测试数学试题云南省2023届高三第一次高中毕业生复习统一检测数学试题北京市第五十七中学2022-2023学年高二下学期3月月考数学试题(已下线)江西省九师联盟2024届高三上学期10月联考数学试题
8 . 已知函数
.
(1)若
恒成立,求实数
的最小值;
(2)证明:有且只有两条直线与函数
的图象都相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a3e92bfb69e10e41f2f05d95a05641.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98dd98c023812b5bae42c3484becb1d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:有且只有两条直线与函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c0ed188d083966baaae94e6b86064f9.png)
您最近一年使用:0次
9 . 已知函数
.
(1)求
的单调区间;
(2)若
有两个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d65edad595cd80754b9cf9626e86fd5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-02-22更新
|
1212次组卷
|
5卷引用:山西省晋城一中教育集团南岭爱物学校2023届高三下学期2月月考数学试题
10 . 已知
,过点
和
的直线为
.过点
和
的直线为
,
与
在
轴上的截距相等,设函数
.则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667160d99fbb37feca6001a20e4e1cf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f5d96189cd76bfe57b65647cfaa150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d363be850487d7cc68074c64f55dee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a775e13b05e0b31aad9b5744fda747e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faef41ef4237d71e748c015b7861c770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eec0c145e060d0bd491b972646f29b4.png)
A.![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.![]() ![]() ![]() |
您最近一年使用:0次