1 . 已知函数
.
(1)求
的单调区间;
(2)证明:
;
(3)若
,且
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e50ead3dafa710129bd59b727bfd756.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29772ffc1a200fb6cd2283aef27e2874.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea134f599285e3d32d2ab3e7186990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225a93c53ca692b1e0a7c9809bbb5326.png)
您最近一年使用:0次
2 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)当
时,求函数
的单调区间;
(3)在(2)的条件下,当
时,
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e5101ed57406f68a0a9372bbd007a0.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/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(3)在(2)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/998485ffeb46a0412ff1a0f814429257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52109b598fb211d3c8ecc3f7718118cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
,
.
(1)当
时,
(i)求曲线
在点
处的切线方程;
(ii)求
的单调区间及在区间
上的最值;
(2)若对
,
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c589325db8016e1566cdcf20d43e288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111324440f372e35f0f37dd29837bea7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
(i)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea9824af71c9da5db5a00ec06063024.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f909328384f9c52134243753d9c954ef.png)
(2)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735fe7737e87152893863b1a11f7a197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0527a896aec4a245945e5edee00deed.png)
您最近一年使用:0次
2023-09-16更新
|
745次组卷
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4卷引用:天津市第二中学2023-2024学年高三上学期开学学情调查数学试题
名校
4 . 设函数
,记函数
有且仅有n个互不相同的零点(
),则当n取到最大值时,实数a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb47838693fde4afcc7627e6c74df02a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e0a9e336769fba32ab7b516f52d0a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
5 . 已知
,函数
,其中e是自然对数的底数.
(1)当
时,求曲线
在点
处的切线方程;
(2)当
时,求函数
的单调区间;
(3)求证:函数
存在极值点,并求极值点
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b86a60faeaffacbc348703f6918e98c.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/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
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2023-05-10更新
|
1923次组卷
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5卷引用:天津市河北区2023届高三二模数学试题
天津市河北区2023届高三二模数学试题天津市第二南开学校2023-2024学年高三暑假开学考试数学试题(已下线)第03讲 极值与最值(七大题型)(讲义)(已下线)专题19 导数综合-1(已下线)第03讲 函数的单调性、极值和最值-【寒假预科讲义】2024年高二数学寒假精品课(人教A版2019)
名校
6 . 下列四个图象中,有一个图象是函数
的导数的图象,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7eee1fb78cfd3cfc568d5450009a910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4886e28e9ecd40f7edd25f25bde28453.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-04-18更新
|
655次组卷
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5卷引用:天津市河北区2022-2023学年高二下学期期中数学试题
天津市河北区2022-2023学年高二下学期期中数学试题四川省广安友谊中学2024届高三上学期9月月考数学(理)试题(已下线)考点9 与二次函数相关的参数问题 --2024届高考数学考点总动员【讲】广西南宁市第二中学2023-2024学年高二下学期期中考试数学试卷(已下线)第03讲 幂函数与二次函数(八大题型)(讲义)
名校
7 . 已知函数
.
(1)求曲线
在点
处的切线方程;
(2)讨论函数
的单调性;
(3)若对任意的
,都有
成立,求整数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61af43b2e572e07e007ff8fa9287766a.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe8d4455774b1fea3ff25747ff3c165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2023-04-06更新
|
3053次组卷
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8卷引用:天津市河北区2023届高三一模数学试题
天津市河北区2023届高三一模数学试题天津市实验中学滨海学校2022-2023学年高二下学期第二次质量调查数学试题天津市朱唐庄中学2022-2023学年高三下学期6月模拟数学试题(已下线)重难点突破10 利用导数解决一类整数问题(四大题型)天津市滨海新区塘沽第一中学2024届高三上学期第一次月考数学复习卷3(已下线)上海市徐汇中学2023-2024学年高三上学期期中考试数学试题变式题16-21(已下线)专题2-7 导数压轴大题归类-2天津市北辰区朱唐庄中学2024届高三模拟预测数学试题
8 . 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/c8feff5470470b8f26c5b1959b41927e.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe949633714dd391eb6d808ee3457d0.png)
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2023-02-22更新
|
1602次组卷
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2卷引用:天津市河北区2022-2023学年高三上学期期末数学试题
名校
9 . 设
,
.
(1)当
时,求曲线
在点
处的切线方程;
(2)若对
,有
,求
的取值范围;
(3)设
在
中有两个零点
,
,证明:
随着
的增大而减小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e91d5400772001006982384a78ce268b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848c33e3506416358d9f0d3ee66f67a9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348551d9ea36d82fab80ae54df9d6c89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89f4eff3125c5e63a994ba1ad5be58e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3907da01aa2971e05262ecf58bafe27d.png)
(2)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311ff26a0cb99d45aaa85ec23a5505f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b817338735d4c23394d6601a7ea4ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f1b4e037116928fd60f5892a211819.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b0305f69331f9bbd5bbcecfc2a694c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95d4b8e7713f727e2c5d8cc30e50e28d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1019d4ad2e3fb4a7abb66e0e9e55b556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
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解题方法
10 . 设函数
,其中
.
(1)若
,求
的单调区间;
(2)若
,
(ⅰ)证明:
恰有一个极值点;
(ⅱ)设
为
的极值点,若
为
的零点,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f30983749e441d75a4906986e142ac5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848c33e3506416358d9f0d3ee66f67a9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b08650d86e207ceded5c8abbfd2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f42fac6e4c5c1b5834bca8f1e8163b.png)
(ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
(ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/015740ce0b7022cf0a5503747c020999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12a4eecd249473a831d0ee472470240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fbfc2b58374e9608973ce3b108726b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b8433690ac98d370f532e71c3383f4.png)
您最近一年使用:0次
2022-10-18更新
|
574次组卷
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4卷引用:天津外国语大学附属外国语学校2021-2022学年高三上学期结课检测数学试题
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