解题方法
1 . 利用曲线的切线进行放缩:设
上任意一点
的横坐标为
,则过该点的切线方程为
,即
,由此可得与
有关的不等式
,其中
,等号当且仅当
时成立;设
上任意一点
的横坐标为
,则过该点的切线方程为
,即
,由此可得与
有关的不等式:
,其中
,等号当且仅当
时成立,设
是
在点
处的切线
(1)求
的解析式
(2)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa18838a13fda4e45612c32cdf98b71.png)
(3)设
,若
对
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63fbb4aa41ac2ae85f8f01175d56973c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbe9fd326374f2b6e740b6af358e5477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad040ae0fab73f5dd7b1af48cd3b5f93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888e7018ffc0049cd7c8eef74af0365d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc59b8f30866d2518b2fcf51072c61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80e266dbe1c3244001a75a8cd9cb0576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7afb62af76c4655a9e7203617079c8d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4c7d5aee3615cdb65b3dd4e24da7bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee3ff7fe9f4a53f93ef0b825b6bf0c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bca6c04ec232aa3ecc1268289271654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1be7302f2e9ff02fee3fcf26e77b1c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/428d922e63d8a0838da6fdacee919ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa18838a13fda4e45612c32cdf98b71.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bafed5b670d33e0fb3bc7bd4dd46f8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0769db255cf03e3e213d629970ca70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2 . 已知函数
(
为常数),记
.
(1)若函数
在
处的切线过原点,求实数
的值;
(2)对于正实数
,求证:
;
(3)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139d335a1800d7441b5c9f8e1202b1e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ba1216bab872fd6bf1b93db0bddb1f1.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)对于正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e2de772d89faaacc8cb3fc92a36412.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a73be8df38d747c2da62c43b2680b3.png)
您最近一年使用:0次
解题方法
3 . 对于函数
,
和
,
,设
,若
,
,且
,皆有
成立,则称函数
与
“具有性质
”.
(1)判断函数
,
与
是否“具有性质
”,并说明理由;
(2)若函数
,
与
“具有性质
”,求
的取值范围;
(3)若函数
与
“具有性质
”,且函数
在区间
上存在两个零点
,
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02059edf02fba0e7c62b7c2a48ef1184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bed7a0e7e7a3b49b4cd2e777a64e9061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a573996f5d4b27434a4491928b59f301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e450d0e48276909b7387fb576df4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e93815f534a9ba003799aef2a53a242.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53224898de85a85058ad336490bbbaa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49636685bca80ed0864d65d829973f8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/798548b5fbb631a0828621581a741f06.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a151adfdf0446b1ac074bca90076df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaae91ed6da60e86e3bb9b3eb7e03e60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba0154a5c65b0b304c7e4df2e738f78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e93815f534a9ba003799aef2a53a242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb8ca1f5da558af68ebe76d985dbbe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b96ee0875a6bcaf9371fb9cfd7eae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.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/04133adb6f1562d859510c9771b2e545.png)
您最近一年使用:0次
4 . 已知定义在
上的函数
的导数满足
,给出两个命题:
①对任意
,都有
;②若
的值域为
,则对任意
都有
.
则下列判断正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d953ea0a5a6b535307b0230b673db30.png)
①对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd423a80d5b6fea8753fa1813cfbcc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5f0ba205794d6fbb4a6b4d4ad6a499c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acde29845a8cbac1e6573ccca56e3756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9587df831df1af5e7dd6be5fdc7bd8ce.png)
则下列判断正确的是( )
A.①②都是假命题 | B.①②都是真命题 |
C.①是假命题,②是真命题 | D.①是真命题,②是假命题 |
您最近一年使用:0次
解题方法
5 . 已知常数
,设
,
(1)若
,求函数
的最小值;
(2)是否存在
,且
,
,
依次成等比数列,使得
、
、
依次成等差数列?请说明理由.
(3)求证:“
”是“对任意
,
,都有
”的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df71f8b32945f3915dd2a0b72593bed.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1757236a5ef1fc70a18f31d6d2438b18.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/dc9769116ec47353514e6b7fb7b17216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/542893790445d6d888d9ff91fd215c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1e5fb2d54a62f243bd5936a3f60386.png)
(3)求证:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a878fd5a7104a7f42770a19097d56457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fd7af568e3d9f444beb0ff41426477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a620b284ae80049376c7a7c9afab1f62.png)
您最近一年使用:0次
2024高三·上海·专题练习
解题方法
6 . 已知函数
,
,
.
(1)当
时,曲线
在
处的切线与直线
平行,求函数
在
上的最大值;
(2)当
,
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3917084c1cd71dc3189470d443c831e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e2b52ffaa094404150fae1422f3cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6efe5ee17b073ed23543464740fe7305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3aa3adcb154f6144903d456289ecb0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b4e7aafb01b2104404fc9f0e5205c2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e14206c7d228a7c2259a7b27da8813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0354c8a10b4d508c0cc6c4d1af6ce5.png)
您最近一年使用:0次
名校
7 . 已知函数
,取点
,过其作曲线
切线交
轴于点
,取点
,过其作曲线
作切线交
轴于
,若
,则停止操作,以此类推,得到数列
.
(1)若正整数
,证明 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/456ed50e1ec3e101f32e930614eebcf9.png)
(2)若正整数
,试比较
与
大小;
(3)若正整数
,是否存在k使得
依次成等差数列? 若存在,求出k的所有取值,若不存在,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590eeefa9b43063edc41ac94f5e02956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b707db9c9766efcc91c87824399b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590eeefa9b43063edc41ac94f5e02956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0b0c4e9dcbfc7a5d04f62fc547ec09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5465bc85798c3bfc7905e58578d251c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590eeefa9b43063edc41ac94f5e02956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b0a15fde3d36d7530e70cc4a5730ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a1aca2793cb07162e29c75a388fe70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)若正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/456ed50e1ec3e101f32e930614eebcf9.png)
(2)若正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf1e4c54010243a8f6c9a1c8482143.png)
(3)若正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835c74bbb8c61dd2d2f008664a8c8810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41dd42e4f493477fb0f36137893d4d06.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
.
(1)讨论
的单调性;
(2)若存在不相等的实数
,使得
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a039b2a1a72d852b992f2d7ee2a20a9e.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若存在不相等的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859458471c86ae39e0cc42d2d960d03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ed4a292f37d53e6d519d5c70b898e8.png)
您最近一年使用:0次
2023-12-30更新
|
1366次组卷
|
7卷引用:第五章 导数及其应用 (压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)
(已下线)第五章 导数及其应用 (压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)河北省沧州市泊头市第一中学等校2024届高三上学期12月省级联测考试数学试题河北省2024届高三上学期12月省级联测数学试题河南省豫西南联考2024届高三上学期期末数学试题(已下线)第04讲 导数在研究函数中的应用-【寒假预科讲义】2024年高二数学寒假精品课(人教A版2019)河北省石家庄市新乐市第一中学等校2024届高三上学期省级联测数学试题(已下线)专题10 导数12种常见考法归类(2)
名校
解题方法
9 . 已知函数
(其中
为自然对数的底数).
(1)当
时,试求函数在
上的最值;
(2)若对任意
,不等式
恒成立,求实数
的取值范围;
(3)设
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c1cbf7f38ac967d545116f95cd469da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dcd143a57a268a5a8ef486e2a4d5c0a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc19da519289b0bce1e206cd1ce022e0.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0ef5a0f806510d2d74492a44dbc721.png)
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6卷引用:上海市宜川中学2022-2023学年高二下学期数学期末模拟测试卷2
上海市宜川中学2022-2023学年高二下学期数学期末模拟测试卷2(已下线)专题02 导数及其应用(八大题型+优选提升题)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)(已下线)专题09 导数及其应用 压轴题(六大题型)-备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)(已下线)第10讲:导数期末题型突破(单调性、不等式、零点、恒成立)(已下线)高二下学期期末数学试卷(提高篇)-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第三册)(已下线)高二下学期期末复习解答题压轴题二十二大题型专练(2)
名校
解题方法
10 . 关于函数
.
(1)讨论函数
的单调性;
(2)若
在
处的切线垂直于直线
,对任意两个正实数
,
,且
,有
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ff251cda384c3a65111ba37e8c7b0e.png)
(1)讨论函数
![](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/c2c3091b94ba135ae28c882c9b71aacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42498f6e0fc9a61c9857b70a87f02c5e.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/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859458471c86ae39e0cc42d2d960d03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7847abd5a830ff448f260b5107ac52.png)
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3卷引用:第五章 导数及其应用 单元复习提升(4大易错与4大拓展)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)
(已下线)第五章 导数及其应用 单元复习提升(4大易错与4大拓展)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)云南省曲靖市第一中学2024届高三上学期第四次月考数学试卷(已下线)特训03 一元函数的导数及其应用 压轴题(七大母题型归纳)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)