已知函数
.
(1)若
,求曲线
在点
处的切线方程;
(2)若
恰有三个零点,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3a3e1d9f785f24c0c39d74dbdb769d9.png)
(1)若
![](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)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
23-24高二下·广东深圳·期中 查看更多[4]
广东省深圳市光明区光明中学2023-2024学年高二下学期期中考试数学试题广东省深圳市光明区高级中学2023-2024学年高三下学期5月模拟考试数学试题陕西省商洛市柞水中学2024届高三下学期高考模拟预测文科数学试题(已下线)专题09 导数与零点、不等式综合常考题型归类--高二期末考点大串讲(人教B版2019选择性必修第三册)
更新时间:2024-06-20 11:37:56
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解答题-证明题
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较难
(0.4)
【推荐1】已知函数
(
为自然对数的底数).
(1)若函数
的图象在
处的切线为
,当实数
变化时,求证:直线
经过定点;
(2)若函数
有两个极值点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9cc60ba0cf582e2c7f7c1bde414dbe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解答题-问答题
|
较难
(0.4)
【推荐2】设函数
为常数.
(1)当
时,求函数
的图象在点
处的切线方程;
(2)若函数
有两个不同的零点
,
,
①当
时,求
的最小值;
②当
时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c59f64a722d8057e571002ce0894d3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497382b74c5322ede61e67f99ea85137.png)
(2)若函数
![](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)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54700061d9f312959c7159c268dede44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
您最近一年使用:0次
解答题-证明题
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较难
(0.4)
名校
【推荐1】设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb2b1aaa9beae3a23b1042cf8ff47c8a.png)
,
(1)讨论
的单调性;
(2)若函数
有两个零点
、
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb2b1aaa9beae3a23b1042cf8ff47c8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829589b2af245e70166896a1c8e35853.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](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/3d10b77f7e61b742705663140e714630.png)
您最近一年使用:0次
解答题-问答题
|
较难
(0.4)
名校
【推荐2】已知函数
.
(1)求曲线
在
处的切线方程;
(2)若
,讨论曲线
与曲线
的交点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae2ff77b0364d1d446008e48ab51402.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e6ace7ba273101018ae81be08c9024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004a9c3c84ff65384fa0b75b9ec2a2cd.png)
您最近一年使用:0次
解答题-问答题
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较难
(0.4)
名校
【推荐1】已知函数
.
(1)若
有两个零点,求
的取值范围;
(2)设
,若对任意的
,都有
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b83f6440736816fbd005866d31b501d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eececc99fc28d96333f6c0f3e04ef742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc4136bd17997e11a7f8abcb19f9018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453d6d3817f54fd73b454c62d8375b3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
【推荐2】已知函数f(x)=ax﹣(a+2)lnx
2,其中a∈R.
(1)当a=4时,求函数f(x)的极值;
(2)试讨论函数f(x)在(1,e)上的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966a5aefa71dfa45ee24d7f9ee8e4c3b.png)
(1)当a=4时,求函数f(x)的极值;
(2)试讨论函数f(x)在(1,e)上的零点个数.
您最近一年使用:0次