名校
1 . 如果曲线
存在相互垂直的两条切线,称函数
是“正交函数”.已知
,设曲线
在点
处的切线为
.
(1)当
时,求实数
的值;
(2)当
,
时,是否存在直线
满足
,且
与曲线
相切?请说明理由;
(3)当
时,如果函数
是“正交函数”,求满足要求的实数
的集合
;若对任意
,曲线
都不存在与
垂直的切线
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749c140afe3f0d42e3cad85909d63938.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06dfc9e95cade14ae9b7fc89519a2dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cedde86fd5b5e93c14ffd9190fc7d7a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cfc27d13b4d07ade4729b481cc95735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/534180efa9c8ffc5ac7cf7f2f035d11c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4526d19896bdff6cb66b4aea9a6ef24d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24600bfcfb91c661eb9d237956e011ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.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/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
2023-04-14更新
|
977次组卷
|
5卷引用:湖北省襄阳市第五中学2023届高三下学期适应性考试(一)数学试题
湖北省襄阳市第五中学2023届高三下学期适应性考试(一)数学试题上海市闵行区2023届高三二模数学试题(已下线)专题03 导数及其应用(已下线)专题02 函数及其应用(已下线)专题08 平面解析几何-学易金卷
名校
解题方法
2 . 已知直线
与函数
的图象恰有两个切点,设满足条件的
所有可能取值中最大的两个值分别为
和
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae96f5020aef5aef03ec7f406460f608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2c16ebe6eb55f7bc40f304d1a9819af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200c21c7c8fb88832addad8457ca8c11.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-04-13更新
|
4037次组卷
|
6卷引用:湖北省武汉市2023届高三下学期四月调研数学试题
湖北省武汉市2023届高三下学期四月调研数学试题(已下线)模块六 专题3 易错题目重组卷(湖北卷)(已下线)专题05 三角函数-1广东省肇庆市肇庆中学2023届高三下学期4月月考数学试题(已下线)压轴小题15 三角函数的切线问题(已下线)专题10 切线问题(过关集训)
名校
解题方法
3 . 已知
,且0为
的一个极值点.
(1)求实数
的值;
(2)证明:①函数
在区间
上存在唯一零点;
②
,其中
且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aaf8922b1b6e2a4366bbd142ad447b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd531902180b2316d92936e1d1c5219d.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f759e5772fb6972efa066f9d0ea363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
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2023-03-24更新
|
3421次组卷
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9卷引用:湖北省武汉市武昌区2022-2023学年高二下学期期末数学试题
湖北省武汉市武昌区2022-2023学年高二下学期期末数学试题山东省烟台市2023届高三一模数学试题山东省德州市2023届高考一模数学试题专题07导数及其应用(解答题)江苏省南京市临江高级中学2023届高三下学期二模拉练数学试题广东省深圳市福田区红岭中学2023届高三第五次统一考数学试题四川省宜宾市叙州区第一中学校2023-2024学年高三上学期10月月考数学(理)试题(已下线)重难点突破09 函数零点问题的综合应用(八大题型)(已下线)第九章 导数与三角函数的联袂 专题四 利用导数证明含三角函数的不等式 微点1 利用导数证明含三角函数的不等式(一)
名校
4 . 在
中,
是
外一动点,满足
,设
,则下列结论正确的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/c7b0f670-66c4-4872-afbe-6e518519b4e0.png?resizew=127)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5cb0c151c65b03e17996dbc13c29000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a8cb4c14a70137ab4ebc08e1e40568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4a41cf2b61cb7dd54ba549a549694b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/c7b0f670-66c4-4872-afbe-6e518519b4e0.png?resizew=127)
A.![]() |
B.设四边形![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
名校
5 . 在
中,
是
中点,
是射线
上的一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/81a83048-546d-475e-8ec7-7ac6de245317.png?resizew=369)
(1)如图1,连接
并延长交
于点
,求
的值;
(2)如图2,
交
于点
,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/81a83048-546d-475e-8ec7-7ac6de245317.png?resizew=369)
(1)如图1,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab17635a999236e8d2e35017a208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e00e7e28f754e518812e746b9be245da.png)
(2)如图2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aa73b8b8f7a9ed8d505b81eb7b3f521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856ddcafb0a8610ed9a95eff0f41e6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d4d78dce0cf121e288749e58b1924d.png)
您最近一年使用:0次
名校
6 . 若关于
的一元二次方程
有两个不相等的实数根
,且
.
(1)下列说法正确的有__________ .(将正确选项的序号填在横线上)
①若
,则
,
②
,
③若
,则
,
④若
,则
.
(2)某数学兴趣小组为了增加此题的趣味性,将题目改成:若关于
的方程
有两个不相等的实数根
,且
,其中
均为整数,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b800b7d6a688abf8a3018c133cec9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5ffa21fddc7c55d35f13435792b2d4.png)
(1)下列说法正确的有
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fe3251e054fe97089806ba7033f802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f75807858b7804a1ad2039c41f323a18.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/badd7f3edb52106b897fe62c9e9ada2e.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4d57bdb85ad21a427ebc3126fab41ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c56b1ee18c6809b339d980671b4d09a.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a066bbbcf164565325c66d9e5f500d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1adacd10539c74b82fc1e6e88ea6f6.png)
(2)某数学兴趣小组为了增加此题的趣味性,将题目改成:若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9c0dce1f975d1203a1bff7580a892d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097f28b6443848c98413364953c37ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数
,将
的所有极值点按照由小到大的顺序排列,得到数列
,对于正整数n,则下列说法中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe71580fe0a6129ae696dd23cf32a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-02-19更新
|
5096次组卷
|
11卷引用:湖北省武汉市2023届高三下学期二月调研数学试题
湖北省武汉市2023届高三下学期二月调研数学试题福建省厦门双十中学2023届高三高考适应性考试数学试题重庆市长寿中学2022-2023学年高三下学期3月月考数学试题广东省佛山市南海区石门中学2022-2023学年高二下学期第一次质量检测数学试题(已下线)模块六 专题3 易错题目重组卷(湖北卷)广东省广州市执信中学2022-2023学年高二下学期期末数学试题广东实验中学2024届高三上学期第一次阶段考试数学试题(已下线)第九章 导数与三角函数的联袂 专题四 利用导数证明含三角函数的不等式 微点4 利用导数证明含三角函数的不等式综合训练(已下线)广东实验中学2024届高三上学期第一次阶段考试数学试题变式题11-14(已下线)函数的应用(已下线)专题23 导数及其应用小题
8 . 若函数
,
的图象与直线
分别交于A,B两点,与直线
分别交于C,D两点
,且直线
,
的斜率互为相反数,则称
,
为“
相关函数”.
(1)
,
均为定义域上的单调递增函数,证明:不存在实数m,n,使得
,
为“
相关函数”;
(2)
,
,若存在实数
,使得
,
为“
相关函数”,且
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1be7302f2e9ff02fee3fcf26e77b1c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475963eea170ff0bbdaf2f0b706dfc34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64d924836b4292239d9726c6473d7f5.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64d924836b4292239d9726c6473d7f5.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e621a08099134be54e682f5724ff4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9d03c536b2d539d4051d663a77a200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a916811b6ae474bce19ce732cf401e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64d924836b4292239d9726c6473d7f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495021c7da1c77e6ed1d1dd30e0be7bc.png)
您最近一年使用:0次
2023-02-11更新
|
2395次组卷
|
4卷引用:湖北省武汉市华中师大一附中2023届高三下学期第二次学业质量评价检测数学试题
名校
9 . 已知直线l与曲线
相切于点
.证明:
(1)l与曲线
恰存在两个公共点
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbb32c12e8fcdd27cdffa88439cc8af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1282489de3b4916175dd456c8e44b4f4.png)
(1)l与曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbb32c12e8fcdd27cdffa88439cc8af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9504e8c607c37583a51c86327a03785a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea87de72c7d5286122f0843a1265bf28.png)
您最近一年使用:0次
名校
解题方法
10 . 设点A为双曲线
的左顶点,直线l经过点
,与C交于不与点A重合的两点P,Q.
(1)求直线
的斜率之和;
(2)设在射线
上的点R满足
,求直线
的斜率的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b30352c43707c4e54b94ce5b61f2e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27cf818dd484cc4cebd40a5f28eb8e9f.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5671fb25040a712a49e8c8148d67d300.png)
(2)设在射线
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