名校
1 . 已知函数
.
(1)当
时,求
的单调区间;
(2)当
时,若不等式
恒成立,求
的取值范围;
(3)设
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae19d7b49be015e2ef80f1ddc78378a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc895959e9bc92294dc9dd2263dbf0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8d5e61351e8a57f702e9ae66d146d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68207a3154bd827a6647075efda61f70.png)
您最近一年使用:0次
2023-10-07更新
|
735次组卷
|
4卷引用:辽宁省六校协作体2024届高三上学期期中联考数学试题
名校
2 . 设方程
有三个实数根
.
(1)求
的取值范围;
(2)请在以下两个问题中任选一个进行作答,注意选的序号不同,该题得分不同.若选①则该小问满分4分,若选②则该小问满分9分.
①证明:
;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b513d7bdd17b6ead5295a0400d0ab15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2755e84aeb379e0117e278f71ca0a9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)请在以下两个问题中任选一个进行作答,注意选的序号不同,该题得分不同.若选①则该小问满分4分,若选②则该小问满分9分.
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5600c61eb9170becdd342ee5619d412d.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af8a6b51796f510821931ea6a9d9cc50.png)
您最近一年使用:0次
名校
解题方法
3 . 已知
,
,函数
和
的图像共有三个不同的交点,且
有极大值1.
(1)求a的值以及b的取值范围;
(2)若曲线
与
的交点的横坐标分别记为
,
,
,且
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19339e3904e9541ff26b30ae5f1242b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39db4885a3de07c0c77b68a7ae2284e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5e31e2e849031f04a645704837266d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求a的值以及b的取值范围;
(2)若曲线
![](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/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0683e38023f949a0d93d43469d54001.png)
您最近一年使用:0次
解题方法
4 . 已知函数
,
(1)若
,求
的图象在
处的切线方程;
(2)若
对任意的
恒成立,求整数a的最小值;
(3)求证
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b9c594a89167c4dee4bc13e921a4799.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0511338aa078cca149b4eb2645e3a7.png)
(3)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968f8d63599c0206c0374006ba14c717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
您最近一年使用:0次
2023-07-14更新
|
487次组卷
|
3卷引用:辽宁省朝阳市2022-2023学年高二下学期期末数学试题
名校
5 . 已知函数
.
(1)若
,证明:
恒成立.
(2)若
存在零点,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac7ed27e75f300e4fa52db2700f3851.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
2023-06-21更新
|
633次组卷
|
5卷引用:辽宁省抚顺市重点高中六校协作体2022-2023学年高二下学期期中考试数学试题
辽宁省抚顺市重点高中六校协作体2022-2023学年高二下学期期中考试数学试题广东省阳江市2024届高三上学期第一次阶段调研数学试题(已下线)专题突破卷07 导数与零点问题湖南省岳阳市岳阳县第一中学2023-2024学年高二下学期4月期中考试数学试题(已下线)专题3 导数与函数的零点(方程的根)【练】
名校
6 . 已知函数
,
为
的导函数.
(1)证明:当
时,
;
(2)判断函数
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d41c638f95c77a4d09219820af96c95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17562636810999b1c98c5e99b5c3e0dd.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/406d118d8529825ab5b55ce92c68fc0f.png)
您最近一年使用:0次
2023-04-09更新
|
1239次组卷
|
6卷引用:辽宁省县级重点高中联合体2023届高三二模数学试题
7 . 已知函数
,
.
(1)当
时,讨论
的单调性;
(2)若
有三个不同的零点
,
,
,求a的取值范围,并证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fef211e5f110fe567b60ee628d6023f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6442958bd5b5f8ac690b33ea0bccdd0f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c547c64dc542c2d192a6ece476fc9bb.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/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f0370bcf7c4e9b3151cd3c779b2d4.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
.
(1)求
的单调区间;
(2)若
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1b193aa193153eb402df8560778e6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecb4095bd18e708a182db1cc694e55b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31aa19c60f49823139869c42cb3ab15a.png)
您最近一年使用:0次
2023-06-06更新
|
817次组卷
|
3卷引用:辽宁省沈阳市第二中学2023届高三下学期第六次模拟考试数学试题
名校
解题方法
9 . 已知函数
.
(1)若
在
单调递增,求实数
的取值范围;
(2)若
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089e5525f126f26e9f8b8b53e0a03951.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f909328384f9c52134243753d9c954ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c532b5af7b88f1c21a7584cfac5fea6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a6441e45f5fbd82ba8f26c905645b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edacb490a7367b0a82edd39caa1439bd.png)
您最近一年使用:0次
名校
解题方法
10 . 已知函数
.(
为实数)
(1)当
时,若正实数
满足
,证明:
.
(2)当
时,设
,若
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67b6d4c78ed45ea2e5ebe7bea653e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e76fa77d1b0bc4c1af9c8c41bf0dabe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/584eac65ed48d878314dc04ded0b319b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f78ae07b1452e4f9dd8ba93db61d17.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5946a5842575e117663fbbc58e2c79fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85187c85826beeca12137805293fff77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
2023-03-25更新
|
1027次组卷
|
2卷引用:辽宁省协作校2023届高三下学期第一次模拟考试数学试题