名校
1 . 已知函数
.
(1)讨论函数
的单调区间;
(2)当
时,函数
有两个零点
,求
的取值范围:
(3)在(2)的条件下,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/784548dbfa097ef19fd7a4e68739e478.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e189dbc979fad6bf8ca03ac1388cbac0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff60eab72de85437e12806474281612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)在(2)的条件下,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc93e6c831bd03403d423b88746e733.png)
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2024-04-01更新
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3卷引用:江苏省淮阴中学2023-2024学年高二下学期级阶段测试(一)数学试卷
名校
2 . 已知函数
.
(1)讨论
的单调性;
(2)设
为两个不相等的实数,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871bbc0c88332bb2de90f33024da19c2.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530a664e40a51a906ac10e44ff360807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ada0ecff751d0cda00141ef7b598570.png)
您最近一年使用:0次
2023-12-15更新
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2卷引用:江苏省淮安、南通部分学校2023-2024学年高三上学期11月期中监测数学试题
名校
3 . 已知函数
,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93bc6e5a4dc1a380eafe763ea38a5a4f.png)
A.函数![]() |
B.当![]() ![]() ![]() |
C.若函数![]() ![]() |
D.若过点![]() ![]() ![]() |
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2023-11-22更新
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3卷引用:江苏省淮安、南通部分学校2023-2024学年高三上学期11月期中监测数学试题
解题方法
4 . 已知函数
.
(1)若
,函数
有两个极小值点,求实数a的取值范围;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2649544729234c4bb748b4e69a1058e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef118cce5443a4d794561f5ef8e1fcc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/534ffd1dd846f0ac5b8f3747d94f0501.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662c379df3425b32a6140736b24d7c5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec1b78045d80469fabd105afa9334cd5.png)
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解题方法
5 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若
的最大值是
,求实数
的值;
(2)若
有两个零点
,
,求实数
的取值范围,并证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a8e0e3b1c0f12e4453b74367affec29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f06c8ed6a4f4262fd8c82b306e15e3.png)
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解题方法
6 . 已知函数
,
.
(1)若
,证明:
;
(2)若函数
最大值为
,求实数a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a3a8c8122cc4a2163760e7c5edfbba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7750f900b4ba09ad4680d39481dc5ea9.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3901dfd4995fe91bcd1ccc26b5cdfa2b.png)
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2023·江苏南通·模拟预测
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解题方法
7 . 已知函数
,其中a为实数.
(1)若
,求函数
在区间
上的最小值;
(2)若函数
在
上存在两个极值点
,
,且
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384295f05d99dedb5dcee82860226d63.png)
(1)若
![](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/5ed2f490aac02631c2ed9e6b76354a49.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88080215d30285bf416853dd8f5b1365.png)
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2023-05-21更新
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5卷引用:江苏省淮安市楚州中学、新马中学2024届高三上学期期中联考数学试题
江苏省淮安市楚州中学、新马中学2024届高三上学期期中联考数学试题(已下线)江苏省南通市如皋市2023届高三下学期适应性测试(三)数学试题内蒙古赤峰市林东第一中学2023届高三5月数学模拟考试题江西省宜春市樟树市清江中学2022-2023学年高二下学期5月期中考试数学试题内蒙古赤峰市林东第一中学2023届高考数学模拟试题
名校
8 . 设函数
,其中
为自然对数的底数.
(1)当
时,讨论函数
在
上的单调性;
(2)当
时,求证:对任意
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0b6ffc19f1678f3cd5a1a2687f3e8f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e445f608e4a7d8535b100c0199a8ecf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/009935dae2483304749bfa46ceb6eecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2143a6cfd3526c4f5795328baa51b0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/563ed1ebb56e33b5c387f3666be28fa9.png)
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2023-01-01更新
|
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3卷引用:江苏省淮安市郑梁梅高级中学2023届高三二模数学试题
解题方法
9 . 已知函数
,
.
(1)证明:
有且仅有一个极小值点
,且
;
(2)若对任意
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42cd5920c27db7257886fece226833b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4031b540afcd3061f431b735a3c62bb6.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b91a0a580b2483bcd16f916611f81c3.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e0656eee2d8ee838aacfda24a00ad69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
10 . 已知函数
.
(1)讨论函数
极值点的个数;
(2)若
有两个零点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188ea6ee27e5cba8c3d5dde1b95fc3a7.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/ac489f65ab7e23212e432bc245ebf622.png)
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2021-10-26更新
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4卷引用:江苏省淮安市高中校协作体2021-2022学年高三上学期期中联考数学试题