名校
1 . 已知函数
.
(1)当
时,求函数
的极小值;
(2)若
有两个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91640760c55e0eccad337d9786accc5b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](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/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-02-11更新
|
1136次组卷
|
7卷引用:江苏省徐州市2022-2023学年高二上学期期末数学试题
江苏省徐州市2022-2023学年高二上学期期末数学试题江苏省部分重点中学2023-2024学年高三上学期第一次联考数学试题(已下线)高二数学开学摸底考02(江苏专用)-2023-2024学年高中下学期开学摸底考试卷(已下线)第六章 导数及其应用(A卷·知识通关练)(5)(已下线)专题七 导数-2(已下线)拓展十二:导数大题的8种常见考法总结(2)广东省珠海市第一中学2022-2023学年高二下学期3月月考数学试题
名校
2 . 已知函数
.
(1)当
时,求函数
的最小值;
(2)已知
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e661c740d0c0df21ba11eb63c38d4372.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc3e5be1796493161a4df7e28a6f6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b00663732dbf41cb74a9417690c8ee96.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86bba348584d85f6774864803c858e6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3d9eb9fa3af53e28e22e8773078724.png)
您最近一年使用:0次
2023-02-10更新
|
813次组卷
|
3卷引用:江苏省南京市、盐城市2022-2023学年高三上学期期末联考数学试题
3 . 已知函数
.
(1)若
时,
,求实数a的取值范围;
(2)讨论
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edbbda9a94f30acce068e171f3b45cfe.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
名校
4 . 已知函数
,
.
(1)若
,
恒成立,求实数a的取值范围;
(2)判断方程
在
上实根个数,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f954dcb88d2779b3770d2ebb5538f5ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd45497d154d217743389fb848a660d2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
(2)判断方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f26b07074550a4ef7cb7387bc47694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
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2023-02-05更新
|
631次组卷
|
3卷引用:江苏省南京市六校联合体2022-2023学年高三下学期1月联考数学试题
名校
5 . 已知函数
,其中
.
(1)当
时,求函数
的单调区间;
(2)已知函数
(
是自然对数的底数),若
,曲线
与曲线
都有唯一的公共点,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fad2f686d1dc1bd946b29836ff52ca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23e6083bfcf557ec745a068dd2d35a0.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187cbe94f239c4b6bab700b46477ab6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93810314c2e788ae6e349759356a59c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
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2023-02-04更新
|
583次组卷
|
3卷引用:江苏省南京师范大学附属中学江宁分校等2校2022-2023学年高三上学期期末联考数学试题
名校
解题方法
6 . 已知函数
,
.
(1)若
的最值和
的最值相等,求m的值;
(2)证明:若函数
有两个零点
,
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ef16b162b3ecc408250c12958760f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76bbebc58f3541be136d3955000c23a7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)证明:若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4633de9335d15d7685bdecb007a3678c.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/bb3dec609e7539997a6a9c4590695c60.png)
您最近一年使用:0次
2023-02-03更新
|
1283次组卷
|
10卷引用:江苏省扬州市高邮市2022-2023学年高三上学期期末联考数学试题
江苏省扬州市高邮市2022-2023学年高三上学期期末联考数学试题江苏省南京市第一中学2022-2023学年高二下学期3月月考数学试题宁夏银川一中2023届高三下学期第五次月考数学(理)试题四川省成都市玉林中学2023届高三二诊模拟理科数学试题(二)河北省行唐启明中学2022-2023学年高二下学期3月月考数学试题北京市海淀区中国人民大学附属中学2022-2023学年高二下学期期中数学复习试题(2)四川省仁寿县铧强中学2023届高三三模文科数学试题四川省仁寿县铧强中学2023届高三三模数学(理)试题四川省南充高级中学2022-2023学年高三第九次月考考试数学文科试题湖南省常德市临澧县第一中学2024届高三上学期第五次阶段性考试数学试题
7 . 已知函数
,
为其导函数.
(1)若
,求
的单调区间;
(2)若关于
的方程
有两个不相等的实根,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0c5b2f883e278d911981efcf4ab19dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a903745cd2cb536443d07579b606ece5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-02-03更新
|
1362次组卷
|
9卷引用:江苏省南京市金陵中学2024届高三上学期期末模拟数学试题
解题方法
8 . 已知函数
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99bd7cce340f3ac9295c6bfd74826796.png)
(1)求实数
的值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)若关于
的方程
有
个不同的实数根
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c18ad0116ba9434c654148f5f1a0ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99bd7cce340f3ac9295c6bfd74826796.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976d18a5396ba232f0aa38d136f1d749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b916df8bdd03ba4a31c0b8470d13436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca13a93b5f401c0d39ba52b0cffcb0.png)
您最近一年使用:0次
解题方法
9 . 已知函数
,
.
(1)当
时,求
的极值;
(2)当
时,设函数
的两个极值点为
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69fa74abdd16494cb8a5ab3acdf1a0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08290af79305df59bc0a1fc2b7c4f7c5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b624d88827e92e12bc0a8f1067cbe72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41c6b9fa72109ba69163a5c6b7874a2.png)
![](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/b28043e7a186ba6ce80ed2570ece7812.png)
您最近一年使用:0次
10 . 已知函数
.
(1)若
有两个零点,求a的取值范围;
(2)若方程
有两个实数根
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c207efd83d75c1f69237d97616c726.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a29249fe99b88f7ffd909777d90beea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0aa8db402d105b72847128f029ed079.png)
您最近一年使用:0次