1 . 已知函数
.
(1)讨论函数
的单调性;
(2)当
时,若
且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4289047be9768c8d25f860fc70389c73.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.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/03ca13a93b5f401c0d39ba52b0cffcb0.png)
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2 . 设函数
.
(1)
时,求曲线
在点
处的切线方程;
(2)证明:
至多只有一个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa6b2c5d246bf027d5face4a86cc5ab.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
名校
3 . 已知函数
.
(1)求曲线
在
处的切线方程;
(2)当
时,求函数
在
上的最小值;
(3)写出实数
的一个值,使得
恒成立,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae77c5783d158610c60c39bb7759c225.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf8eca68c4c7478f412183aa275fc7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce7bf4affe75671a45a04c51e881676.png)
(3)写出实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81ed7f6a4475e0fa682fa81ee747da3.png)
您最近一年使用:0次
2024-02-27更新
|
794次组卷
|
4卷引用:北京市海淀区北京一零一中2023-2024学年高三下学期统考四(开学考)数学试题
名校
4 . 已知函数
.
(1)讨论
的单调性;
(2)若方程
有两个不相等的根
,且
的导函数为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fc2a19b46639a8c5ed29281a867ba73.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e924f5b6b26534b7eea00660e9d0d9a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/133c30d6ca96a4d8de293da20fbe8f22.png)
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2024-02-27更新
|
1007次组卷
|
7卷引用:湖南省三湘创新发展联合体2023-2024学年高三下学期2月开学统试数学试题
名校
解题方法
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6b39ee1316fd4f1c3ad78cf32f1371.png)
(1)若函数
的最小值为0,求
的值;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6b39ee1316fd4f1c3ad78cf32f1371.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d1b80fdf5d4097cd72bb6c5a583fb0.png)
您最近一年使用:0次
2024-02-27更新
|
599次组卷
|
4卷引用:福建省莆田第一中学2023-2024学年高二下学期期初考试数学试卷
福建省莆田第一中学2023-2024学年高二下学期期初考试数学试卷(已下线)专题4 导数在不等式中的应用(讲)福建省连城县第一中学2023-2024学年高二下学期4月月考数学试题(已下线)模块一 专题4 《导数在不等式中的应用》(苏教版)
名校
解题方法
6 . 已知函数
.
(1)证明:对任意的
,都有
.
(2)若关于
的方程
有两个不等实根
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f991208bb21eb52f9bab02d90dd64b0d.png)
(1)证明:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047056c99b39c70fa40d3c8178e5b631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43920f5171ed31db2520ef00e4c5fc24.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb2e46f49adba6036e2624639a1b966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b677fee269b63c8ae43f0f6ddb5c70.png)
您最近一年使用:0次
名校
7 . 已知函数
.
(1)当
时,求
的单调区间;
(2)若
时,
,求a的取值范围;
(3)对于任意
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27862c9517dbb4eb17a6725eb142969.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(3)对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1af027bd16e380d3be03a9761ca56055.png)
您最近一年使用:0次
2024-01-18更新
|
2008次组卷
|
9卷引用:山东省济南市2024届高三上学期期末学习质量检测数学试题
解题方法
8 . 已知函数
,其中
为自然对数的底数.
(1)当
时,判断函数
在区间
上的单调性;
(2)令
,若函数
在区间
上存在极值,求实数
的取值范围;
(3)求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307a38dc2b519cda3f97fc1c0d012178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b2b756a6909d8bc5692711d5626ba3f.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c765461ae1a6c70f5cbdcb6c932a22b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
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解题方法
9 . 已知函数
且
恒成立.
(1)求实数a取值的集合;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50ae60a5066382a41ab365ee014ed899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
(1)求实数a取值的集合;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ab301cd91aa2a5cf9b5fd1365d17cb.png)
您最近一年使用:0次
名校
10 . 已知函数
.
(1)当
时,讨论函数
的单调性;
(2)若函数
有两个不同的极值点
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f2833c86b4a21cfb25ec445b66fc4a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b64b1a6ad90a44dd02e91a62f2c0364.png)
您最近一年使用:0次