1 . 已知函数
.
(1)求函数
的单调区间;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f21f95f814279f3f7181358e516dcdc3.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19178309da9b8f4507996879a3db7010.png)
您最近一年使用:0次
名校
2 . 已知函数
.
(1)讨论函数
的单调性;
(2)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea7114e419879e46c50040dc83df364.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/625a079b32205e84bf97be8879fa45eb.png)
您最近一年使用:0次
2023-12-25更新
|
1102次组卷
|
10卷引用:四川省成都市2024届高三一模数学(理)试题
四川省成都市2024届高三一模数学(理)试题(已下线)模块三 大招8 不等式证明——分割与放缩安徽省马鞍山市当涂县第一中学2023-2024学年高二上学期1月期末测试数学试题(已下线)专题1.3 利用导数研究函数的单调性(七个重难点突破)-2023-2024学年高二数学下学期重难点突破及混淆易错规避(人教A版2019)(已下线)重难点06 导数必考压轴解答题全归类【十一大题型】(已下线)专题4 导数在不等式中的应用(讲)(已下线)2023-2024学年高二下学期第一次月考解答题压轴题十六大题型专练(1)(已下线)导数专题:导数与不等式成立问题(6大题型)-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第二册)(已下线)模块一 专题4 《导数在不等式中的应用》(苏教版)(已下线)模块三 专题2 解答题分类练 专题5 导数在不等式中的应用【高二人教B版】
名校
解题方法
3 . 已知函数
.
(1)若
在
上单调递减,求实数
的取值范围;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e240a5e97a7c1b55cf69946c4dc553.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cb56c4d08062c178b706b9e1c7cec5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/035c8e0ab1aeabf3306be201aaaa78a9.png)
您最近一年使用:0次
2023-12-21更新
|
227次组卷
|
2卷引用:河南省湘豫名校2024届高三上学期12月联考数学试题
名校
4 . 已知函数
(
).
(1)若
,求
的图象在
处的切线方程;
(2)若
有两个极值点
,
(
).
①求
的取值范围;
②求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82b6de4b2701fdc0a49f9aab1a17941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若
![](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)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dd083f3324c690633af999efecb6f73.png)
您最近一年使用:0次
2023-11-29更新
|
877次组卷
|
4卷引用:河南省新高中创新联盟TOP二十名校计划2024届高三上学期11月调研考试数学试题
解题方法
5 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)当
时,求使
恒成立的最大偶数
.
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db26990def13099db22a6630a84b71f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9807631136840cb8da536aae933cbedf.png)
您最近一年使用:0次
解题方法
6 . 已知函数
,
.
(1)求函数
的图象在点
处的切线方程;
(2)求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/462ea72d493573e7ce45bde7a4bbb160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d672d1920ec68593170f90209ffb5521.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e82c4003d20b36777f7aea584e3dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05fce924911d5ed93147dfce9e41c2b0.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数
.
(1)若
在R上单调递增,求实数a的取值范围;
(2)当
时,证明:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b760ef16b1172e7ab8068ddad0b356a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbbbc61ec7004b8404dc6bf724aa83ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee1fedd70e9f8422a3aa5a56ff3f0dc5.png)
您最近一年使用:0次
2024-04-12更新
|
533次组卷
|
4卷引用:山东省烟台市2023届高三二模数学试题
8 . 已知直线
与曲线
.
(1)若
与
交于
,
两点,点
,直线
与
的斜率之积为1,证明:直线
过定点;
(2)若
与
相切于点
,过点
且与
垂直的直线分别交
轴、
轴于
,
两点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13d0ee6c655032e821c650ff3f6a482.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9697f70515f776ae4995c9671327f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2da812df93d79f45084f076cb14bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb80d86dd5ef8239fe0d60a4c8a6f03d.png)
您最近一年使用:0次
名校
解题方法
9 . 已知函数
.
(1)若
在定义域内为单调递减函数,求a的取值范围;
(2)求证:当
且
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9bc3a160c11e115aff413f9ceaec70b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58427d5aa7deeca47c8789241913f30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5e026a565c24617edc36f82fd85e63.png)
您最近一年使用:0次
2024-01-10更新
|
539次组卷
|
3卷引用:河北省石家庄市第二十七中学2024届高三上学期金太阳联考数学试题
10 . 设函数
.
(1)当
,
时,
①求
在
处的切线方程;
②求证:当
时,
;
(2)当
时,已知
为函数
的两个零点(
为
的导数),求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5660c7eb9795d81e7854875765df29b0.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3320a13248a3a1208ff6ee85c9d26f36.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
②求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcac1e85463a3177f487d896b3d1d24c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57318ea12371c9fc9a7aeba5deb1c549.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac02d94e59022a5499b6755f8d8f0b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383c5fd6b3d4619c9292d2560046285c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/936ab057c74ffcee55426a1f0d7e8e6e.png)
您最近一年使用:0次