名校
解题方法
1 . 若函数
在定义域内存在两个不同的数
,
,同时满足
,且
在点
,
处的切线斜率相同,则称
为“切合函数”.
(1)证明:
为“切合函数”;
(2)若
为“切合函数”(其中
为自然对数的底数),并设满足条件的两个数为
,
.
(ⅰ)求证:
;
(ⅱ)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.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/abf7c745cd02f4620a175cf00ec85e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24a2c53e3b0b1c08803e95419f909d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecaca8409b3f51d22667a14559c58ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe0de54dfc96a2291e8d5e56676eabc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fb46178ba0560d96bd3a05891505b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c20b8bd265b07dd90690ad4e349c6dc.png)
(ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84cde09c609543feedc2e0c11992b2bd.png)
您最近一年使用:0次
2024-01-03更新
|
1045次组卷
|
4卷引用:重庆市南开中学校2024届高三上学期第五次质量检测数学试题
重庆市南开中学校2024届高三上学期第五次质量检测数学试题重庆市沙坪坝区南开中学校2024届高三上学期第五次质量检测数学试题江西省赣州市南康中学2024届高三上学期新高考“七省联考”考前数学猜题卷(一)(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编
名校
解题方法
2 . 设函数
,
.
(1)①当
时,证明:
;
②当
时,求
的值域;
(2)若数列
满足
,
,
,证明:
(
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df075cd20f79486d88d80ee12fc897d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5883f63cdc68865d41cc935b7b39557d.png)
(1)①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5cdde751120c6deab563a6f7f8cf05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffa28c7f519c1c85c0a3cad23b2e6cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ebb32ddcd84417fc992dad3ccba8894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adfbda63ad7cfeb044819141f1924598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
您最近一年使用:0次
2023-12-30更新
|
1080次组卷
|
4卷引用:重庆市育才中学、万州高级中学及西南大学附中2024届高三上学期12月三校联考数学试题
重庆市育才中学、万州高级中学及西南大学附中2024届高三上学期12月三校联考数学试题广东省广州市华南师大附中2024届高三上学期大湾区数学预测卷(一)(已下线)四川省成都市第七中学2024届高三上学期期末数学(理)试题(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编
名校
3 . 设
是定义在
上的函数,若存在区间
和
,使得
在
上严格减,在
上严格增,则称
为“含谷函数”,
为“谷点”,
称为
的一个“含谷区间”.
(1)判断下列函数中,哪些是含谷函数?若是,请指出谷点;若不是,请说明理由:
(i)
,(ii)
;
(2)已知实数
,
是含谷函数,且
是它的一个含谷区间,求
的取值范围;
(3)设
,
.设函数
是含谷函数,
是它的一个含谷区间,并记
的最大值为
.若
,且
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1486d2ae6c7e7904ab47b909039ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adadc4c82ed03710cb917d552ac6e1c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd33dd2e1b404daf7c1cbbf147ab7f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)判断下列函数中,哪些是含谷函数?若是,请指出谷点;若不是,请说明理由:
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65ecb5b1f957213346a78a229314e73f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2323ed90e5321507ae65763db9594b9.png)
(2)已知实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2739d1d7a587d0a327c5b75fcaba9d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7242b2ab643f9470da77e29d043b893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0137d9ccd136186c2fe74a11e42376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f86c67af4135ba55b227485de51d4ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b9c9a559b5ec35dd6bc7abf3f4c8d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27aed40481d951cc4afd5c7c1a470d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94a112fefbaf48adf34edbf3243ee7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b9c9a559b5ec35dd6bc7abf3f4c8d6.png)
您最近一年使用:0次
2023-12-18更新
|
914次组卷
|
5卷引用:上海市浦东新区2024届高三上学期期末教学质量检测数学试题
上海市浦东新区2024届高三上学期期末教学质量检测数学试题2024届高三新改革适应性模拟测试数学试卷二(九省联考题型)(已下线)专题09 导数(三大类型题)15区新题速递(已下线)专题1 导数与函数的单调性(恒单调、存在单调区间、不单调)【练】广西南宁市第二中学2023-2024学年高三下学期5月月考数学试题
名校
解题方法
4 . 已知,椭圆的面积为
(其中,
为椭圆的长半轴长,
为椭圆的短半轴长).若椭圆
:
的左、右焦点分别为
,
,过
的直线与
交于
,
两点,直线
与
的另一交点为
(
,
,
均不与
顶点重合),
的周长为8,
的面积为
.
(1)求
的标准方程;
(2)
为原点,记直线
,
的斜率分别为
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b30489cd9c57a2c6283e0fc36129728c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b52af1d93cf91437881f823ad19623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0407e1f5977d2cb46d362e8362c8816f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95cefb160c373407a49e3a8aee1a228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/023037c7a3e31ba698c39f9b52db2515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5464bc1d5c3cf98043eac02a2fc66a55.png)
您最近一年使用:0次
2023-12-13更新
|
466次组卷
|
2卷引用:四川省达州市普通高中2024届高三上学期第一次诊断性测试数学试题(理科)
名校
解题方法
5 . 已知定义在
的函数
满足:①对
恒有
;②对任意的正数
,
恒有
.则下列结论中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6a8984aa398bf767ccd9a601d77983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a66d161030ad93973d77b1c53dec8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5386d0aff1b962f99b5565adb9a58cbf.png)
A.![]() |
B.过点![]() ![]() |
C.对![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
2023-12-08更新
|
1504次组卷
|
6卷引用:湖北省黄冈市部分普通高中2024届高三上学期阶段性教学质量监测数学试题
湖北省黄冈市部分普通高中2024届高三上学期阶段性教学质量监测数学试题广东省广州市广东实验中学2024届高三上学期大湾区数学冲刺卷(三)江西省抚州市临川第一中学2024届高三“九省联考”考后适应性测试数学试题(一)(已下线)第五章 一元函数的导数及其应用(压轴题专练,精选34题)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第二册)湖南省长沙市明德中学2023-2024学年高二下学期开学考试数学试卷2024届高三新高考改革数学适应性练习(九省联考题型)
名校
解题方法
6 . 已知实数m,n满足
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d4b55b21e776a254f07f56fab5c958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c294fe813bfa5e8ef0c612c7d1d1a9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-11-28更新
|
1143次组卷
|
5卷引用:河南省部分名校2023-2024学年高三上学期阶段性测试(三)(11月)数学试题
河南省部分名校2023-2024学年高三上学期阶段性测试(三)(11月)数学试题江苏省扬州市扬州中学2024届新高考一卷数学模拟测试一(已下线)模块五 全真模拟篇 基础1 期末终极研习室(2023-2024学年第一学期)高三江西省赣州市南康中学2024届高三上学期新高考“七省联考”考前数学猜题卷(一)广东省佛山市第一中学2024届高三下学期开学预测数学试题(一)
2023·全国·模拟预测
解题方法
7 . 已知点P,Q是圆
上的两个动点,若直线OP与OQ的斜率都存在且满足
.
(1)当
时,求PQ的中点M的轨迹方程;
(2)当
时,椭圆
与动直线PQ恒相切,求椭圆C的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1000c40056cb9ed50d7157b8dd998fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08be81d68cd0b6cd737f77f23e77be5e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4561e662151983a27b3e8c8fcc857f06.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6494bb8bce0f3656e612f38031b2c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
您最近一年使用:0次
名校
解题方法
8 . 已知抛物线
:
(
)上一点
的纵坐标为3,点
到焦点距离为5.
(1)求抛物线
的方程;
(2)过点
作直线交
于
,
两点,过点
,
分别作
的切线
与
,
与
相交于点
,过点
作直线
垂直于
,过点
作直线
垂直于
,
与
相交于点
,
、
、
、
分别与
轴交于点
、
、
、
.记
、
、
、
的面积分别为
、
、
、
.若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ec1206d61f9087710805ceadfe04745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129f1d6567bef09b00b7f37894e6dba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4c625a55ef1d2920a0605d52c8da23.png)
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9 . 已知
,则在下列关系①
;②
;③
;④
中,能作为“
”的必要不充分条件的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dd00e2f6802c99fb624aa77ebe17d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f72f0a62b1a8614acae64570d8bf1170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b973e2ec0d256343c57ce0c3cd80ab2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65eb4d879e3e80d3195b56b303e331c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485a2d99320384a0857b00ce9ab9e990.png)
A.1个 | B.2个 | C.3个 | D.4个 |
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2卷引用:四川省成都市第七中学2023-2024学年高三上学期期中考试理科数学试题
名校
10 . 已知函数
图象上的点
均满足
对
有
成立,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d14c828a3f9835432279d83c6c331a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2db9a58e185e4fd9c4f86efb24480f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bad5c8a4e4bad474651c0a61de820ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0440bb2a43a6f9669fb5c3703a024989.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() |
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