1 . 已知函数
.
(1)求
在
处的切线方程;
(2)求证:当
时,函数
有且仅有
个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83705741a6c647c78058b58b3802834a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f94c6dd98708d42f4233a04397db41c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
,
.
(1)当
时,求曲线
在
处的切线方程;
(2)求
的单调区间;
(3)设
是函数
的两个极值点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1237be7b7b3712cfe108061534ef7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.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)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2aabc96b7433bba077ceac76d8f0d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00210f79b04a8f6bc1922433d00bc89a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ac3f646599fe63ff886d34750e4e6a.png)
您最近一年使用:0次
2024-01-25更新
|
1820次组卷
|
5卷引用:福建省莆田市莆田第一中学2024届高三上学期第一次调研数学试题
福建省莆田市莆田第一中学2024届高三上学期第一次调研数学试题天津市宁河区2024届高三上学期期末数学试题(已下线)重难点2-4 利用导数研究不等式与极值点偏移(8题型+满分技巧+限时检测)(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(2)(已下线)模块2专题7 对数均值不等式 巧妙解决双变量练
名校
解题方法
3 . 已知函数
.
(1)求曲线
在点
处的切线方程,
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/903f1f0c9ff9bc834d16dfed6359f411.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c069903b3b06877ffa9d6db7fbc5c57.png)
您最近一年使用:0次
2023-12-19更新
|
1852次组卷
|
12卷引用:福建省部分学校2024届高三上学期12月月考数学试题
福建省部分学校2024届高三上学期12月月考数学试题湖北省部分学校2024届高三上学期12月联考数学试题陕西省商洛市2024届高三一模数学(文)试题海南省2024届高三上学期一轮复习调研考试(12月联考)数学试题陕西省商洛市2024届高三一模数学(理)试题山东省潍坊市昌乐第一中学2024届高三上学期12月月考数学试题贵州省遵义市2024届高三上学期12月月考数学试题(已下线)专题2-6 导数大题证明不等式归类-3河南省三门峡市2024届高三上学期第一次大练习数学试题(已下线)模块四 第五讲:利用导数证明不等式【练】广东省中山市桂山中学2023-2024学年高二下学期第一次段考检测数学试题陕西省西安市长安区第一中学2023-2024学年高二下学期期中考试数学试题
4 . 已知函数
,
.
(1)若
满足
,证明:曲线
在点
处的切线也是曲线
的切线;
(2)若
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64263fe2ca48e694c87496d61e63fb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97d51430298d99909a8f673d1039d6f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538f9b0676cc0cd02c09fac51d9e4fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8206742853cbd11f12c833b2f07949ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3c2be7482719651bcf491949681e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b24ab2c1aa0979146fbb30b7d72d6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13bfeb2f86cf0e842ff71c3d21880fe5.png)
您最近一年使用:0次
名校
解题方法
5 . 已知函数
,
.
(1)证明:对于
,
,都有
.
(2)当
时,直线
:
与曲线
和
均相切,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a3199e7b4e66aba9f167701839e94e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfe02fb63c8d651466881d4b85a45b9.png)
(1)证明:对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129450a089ab2e252cd3e229b22df4e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c164755dc2d7cff80fb4c9cffc9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2023-09-19更新
|
633次组卷
|
5卷引用:福建省厦门市湖滨中学2024届高三上学期10月月考数学考试题
名校
6 . 已知函数
.
(1)求曲线
在点(2,2)的切线方程;
(2)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b636844dddba5c8e2a96f34e03c7eddb.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7376dbe3af5f7132e15d0457ac4ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4be9f060f0bad0cd74aed6d3a517e1c5.png)
您最近一年使用:0次
2023-04-14更新
|
262次组卷
|
2卷引用:福建省福州第一中学2022-2023学年高二下学期第三学段模块考试(期中)数学试题
名校
7 . 已知函数
.
(1)求曲线
在
处切线的斜率;
(2)当
时,比较
与x的大小;
(3)若函数
,且
(
),证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e4bdada70f9217234b43e8747a855f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f4241a5db19c15cb647bf520a8570e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e86a442e2b43d732352ea5f44edc4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc27e66b5547d400351b99194496883.png)
您最近一年使用:0次
2023-10-05更新
|
549次组卷
|
8卷引用:福建省部分学校2024届高三上学期10月阶段性考试数学试题
解题方法
8 . 已知函数
,记曲线
在点
处的切线为
,
在x轴上的截距为
.
(1)当
,
时,求切线方程;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e70f9d551b5436e708b405268ea290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27c0ab3e2d7698f082854bafe4174dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/126a0b15e6d9d6c106cdc3aa74a83cd3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d47b5d9bb960850cfc33e252d3d852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266115b42426704177393dff1db45f00.png)
您最近一年使用:0次
名校
9 . 已知函
,
.
(1)讨论
在
的单调性;
(2)是否存在
,且
,使得曲线
在
和
处有相同的切线?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b162223eb963d4fcd51313cf42f6b181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d88e4b98cabf9806bd67e58f98a1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4cfc4049753f02d44f8a0d09353057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971905ea129aec0ca7c325f60260c7e1.png)
您最近一年使用:0次
2023-04-10更新
|
1869次组卷
|
2卷引用:福建省2023届高三毕业班适应性练习卷(省质检)数学试题
名校
10 . 已知函数
.
(1)已知过点
的直线
与曲线
相切于
,求
的值;
(2)已知
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda80a72fcc5fd51a32caee55e6d4f3b.png)
(1)已知过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f2bbe7a96bebd043bb5f3e85e8cd38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/234dac6ab56e10a7550a3659e21a7a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1224aa410c244829cdb45126306bc00.png)
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