解题方法
1 . 已知定义在
上且不恒为
的函数
,若对任意的
,都有
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64541d7f445079207b6f671adc7d662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/649df22b06d6aa4123fcbbba8e759532.png)
A.函数![]() |
B.对![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
名校
解题方法
2 . 已知函数
在
上单调递减,在
上单调递增.记函数
.
(1)写出函数
的单调区间(无需说明理由)及其最小值;
(2)若直线
与函数
和
的图象共有三个不同的交点,从左到右依次记为
,
,
,试证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2399c2a712a2890dcd0b195d3b9f1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6097169b69ad927c38efd7d52ec65f95.png)
(1)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af79f45b5880c72a349500da9d8e118d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c16dac1e9bf5804c8907cbc59014d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6fbfe23e06cc72f33f925dd5ee3351e.png)
您最近一年使用:0次
3 . 设
,
,若a,b,c互不相等,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e34f42b3be15518c29e3689c9fe6d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48044aa6520cdc0688a5e121a94cda1c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-03-01更新
|
612次组卷
|
4卷引用:浙江省绍兴市第一中学2023-2024学年高一上学期期中数学试题
浙江省绍兴市第一中学2023-2024学年高一上学期期中数学试题辽宁省丹东市2022-2023学年高三上学期期末数学试题(已下线)重难点04 指、对、幂数比较大小问题【七大题型】(已下线)专题9 式子大小判断问题(过关集训)
名校
解题方法
4 . 定义在
上的函数
满足:对任意的
,都存在唯一的
,使得
,则称函数
是“
型函数”.
(1)判断
是否为“
型函数”?并说明理由;
(2)若存在实数
,使得函数
始终是“
型函数”,求
的最小值;
(3)若函数
,是“
型函数”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5a7d4a1885b3d02c5aa8e4dc2ec509f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac8cb46c172b9bbd6c21ae026424b3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f5148c90b6d762234102e5bf5ca4c5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66f5ca58bc2555dc2b320a5e29cfe7e.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04beea76c59a6c5b096d8c5a3b77f8a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35612da13321cdec14c185c69e9e0b10.png)
(2)若存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a353a3d7b765d252c8aabdc641fcf7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66f5ca58bc2555dc2b320a5e29cfe7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15cefe8102d06c44e21abd591631e449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d90a00224f84eef1fd26f303d86a914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-02-18更新
|
727次组卷
|
3卷引用:浙江省宁波市2022-2023学年高一上学期期末数学试题
5 . 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:浙江省温州市2023届高三下学期返校统一测试数学试题
名校
解题方法
6 . 已知函数
.设s为正数,则在
中( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f4e87d1dca1b674f88a060cdf8bab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7efade8a0a3ceffd14c2611497d42eaf.png)
A.![]() | B.![]() |
C.三者不可能同时相等 | D.至少有一个小于![]() |
您最近一年使用:0次
2023-01-16更新
|
1601次组卷
|
5卷引用:浙江省强基联盟2022-2023学年高三上学期1月统测数学试题
名校
解题方法
7 . 设函数
(其中
是非零常数,
是自然对数的底),记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08d422069255315cda9300f042592280.png)
.
(1)求对任意实数
,都有
成立的最小整数
的值
;
(2)设函数
,若对任意
,
,
都存在极值点
,求证:点
在一定直线上,并求出该直线方程;
(3)是否存在正整数
和实数
,使
且对于任意
,
至多有一个极值点,若存在,求出所有满足条件的
和
,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33064244eb1291dd64d934b68f579de1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08d422069255315cda9300f042592280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90e6e8340a691b540f1322c0aaa87d77.png)
(1)求对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416d5334e06f6a69817aa4c95ef6b5a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90e6e8340a691b540f1322c0aaa87d77.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e35c498029b87a5fa84a1047a5c2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6f0a55fa53bf5f8e6654897975bcf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b43f4c5b17fb428231e2958c36404b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787559fbe7c04f1e9aca26f3bdf26f71.png)
(3)是否存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8feaf51b5fdc0b7aad38b26f57825712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dded00a646338958d93e8a43bc157a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
2022-12-15更新
|
1014次组卷
|
5卷引用:浙江省杭州市桐庐中学2022-2023学年高三上学期1月期末数学试题
浙江省杭州市桐庐中学2022-2023学年高三上学期1月期末数学试题上海市青浦区2023届高三一模数学试题(已下线)核心考点09导数的应用(1)上海市复旦大学附属中学2023-2024学年高三下学期三模数学试题(已下线)上海市高二下学期期末真题必刷04(压轴题)--高二期末考点大串讲(沪教版2020选修)
名校
解题方法
8 . 已知实数
,且函数
,
,
,
,
,当
时,
的最小值记为
.
(1)若
,求函数
的单调递减区间;
(2)
,
,
,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a380067a20c25338eb0312e8df6c2760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7051b8cbec548d942b62fd290db4460.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383330e8699c6ce53da6c5aaa70097d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/442a82cb501aeda22a086a2fe7ef7cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e9ac469995de3fcccf9300fbe8c68b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edb160b3d56fdc5cb2123cbcac44c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe7341e9d43f8456a913620d9938205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6dd3fa42436802a270cd2ff46ba51d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be555d216bf07f824f3164f05e1cb72.png)
您最近一年使用:0次
2022-11-11更新
|
706次组卷
|
3卷引用:浙江大学附属中学2022-2023学年高一下学期期中模拟数学试题
名校
9 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfee95d6478632175879ca44de045963.png)
A.任意![]() ![]() ![]() |
B.任意![]() ![]() |
C.任意![]() ![]() ![]() |
D.当![]() ![]() |
您最近一年使用:0次
2022-05-26更新
|
2034次组卷
|
4卷引用:浙江省杭州四中下沙校区2023-2024学年高一上学期期中数学试题
浙江省杭州四中下沙校区2023-2024学年高一上学期期中数学试题浙江省十校联盟2021-2022学年高二下学期5月联考数学试题(已下线)专题03函数及其表示-2022年新高三数学暑假自学课精讲精练章节综合测试-指数函数与对数函数
名校
10 . 如图所示,等腰梯形
中,
,
,已知E,F分别为线段
,
上的动点(E,F可与线段的端点重合),且满足
,
.
关于x,y的关系式并确定x,y的取值范围;
(2)若
,判断是否存在恰当的x和y使得
取得最大值?若存在,求出该最大值及对应的x和y;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e921f46d90e43f4517c55832b6280f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c3f33f58f50ec2d5f038e620c3294f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1578eb173c8b9a7a124c988f77a690bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14c37cb57db83fb57e6a0d3a0afa1127.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a5df115177284576970a912b09ba7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916bb2cc1b29574ff95b47567c59ee0c.png)
您最近一年使用:0次
2022-04-03更新
|
1179次组卷
|
8卷引用:浙江省温州新力量联盟2022-2023学年高一下学期期中联考数学试题