1 . 已知函数
(
为实常数).
(1)若
在
上单调递增,求实数
的取值范围;
(2)判断是否存在直线
与
的图象有两个不同的切点,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6923e3721c0e08fd3099c0f386124f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a141e697b1a31a9a4e759984e899a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)判断是否存在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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2 . 已知
,记
的导函数为
.
(1)讨论
的单调性;
(2)若
有三个零点
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35a1a8b0298d7e078e33e81fe3836f47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1278a655c6539ee916af9a1a889f15e.png)
您最近一年使用:0次
名校
3 . 已知函数
有两个不同的零点x1,x2.
(1)当
时,求证:
;
(2)求实数a的取值范围;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4ef50e8e5c2f1608cfe26291e3316b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73200c826a96ef1bd71cd18ac191631b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4d0b816ee9c5573dffcb31c192c9d7.png)
(2)求实数a的取值范围;
您最近一年使用:0次
2023-01-22更新
|
301次组卷
|
4卷引用:广西柳州市第三中学2023届高三下学期2月开学考数学(文)试题
名校
解题方法
4 . 已知
,
.
(1)求
的单调区间;
(2)当
时,若关于x的方程
存在两个正实数根
,
(
),证明:
且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f78ed311a6511c1d64131cd27c2d45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c2e9f55394c820a01639b63513bdc62.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/463de040f7682fa8cb5d8fa2cd6b7d46.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/a2609bbd86aeb222374474ea4acb3e38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7b93a0ee368e333465fdf4ee249e41.png)
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2022-11-18更新
|
501次组卷
|
3卷引用:广西柳州市2023届高三毕业班上学期11月模拟统考数学(理)试题
5 . 已知函数
.
(1)若函数
在点
处切线的斜率等于1,求a的值;
(2)讨论函数
的单调性;
(3)若函数
有两个极值点分别为
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff6ce2f7b19a4dbe417a280f8b7299c0.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.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)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8f76349824db1e05046014d5903da4.png)
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