名校
解题方法
1 . 已知函数
,
,若对于任意的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244af58c69c119a21c512a8ea77e4dac.png)
,使得
恒成立,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d286f10c2662c15a7e6b45394d20f56c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/262077581baf603acf7be972c8afb42e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/244af58c69c119a21c512a8ea77e4dac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032e8dc00cdc96860c9cbf8ac09677fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
2 . 已知函数
的图象在点
处的切线方程为
.
(1)则实数a的值为__________ ;
(2)设
,若
对任意的
恒成立,则k的最大整数值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9087da83d78b737d7ac90458c171d5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc568fbc1480ba87cfdc2b6b3c71200.png)
(1)则实数a的值为
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b034f42a44cb15e6b320f24dd7cdd0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd179a4430d2f13d30bda9a42248ed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0aa2ef928b6e3341d0a0dc6d8055b9.png)
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名校
3 . 已知函数
.
(1)求曲线
在
处的切线方程;
(2)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a44f951eba35ed9b8e78e098fa7d6d8.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2b74d89854116e411c089d053df053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66d61d5f66d68b4c4a2a25fd7103621.png)
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名校
4 . 已知函数
.
(1)求
的单调区间;
(2)若
恒成立,求实数
的取值范围;
(3)求证:
.(
且
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf0751f1d99f7ef325f1ee585523cde.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2aeda5c6f101566159dd4c460b943b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6737a7bb16d98ad402700a3ae0fb9e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
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名校
5 . 已知
在
处的切线方程为
.
(1)求实数
的值;
(2)证明:
仅有一个极值点
,且
.
(3)若
,是否存在
使得
恒成立,存在请求出
的取值范围,不存在请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5387267b6f5965456de8f0e0bdf964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58153bf3fdc83363cb5a23a2740d3778.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dec9c729c13d5db8e8929f726c3abcb.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cae1d9c7098a778798abc2e7b60151a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfaf5afd77bd894df1e1a672040de990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
6 . 设函数
,则
是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f438eca2954862a6a7dc020ffeb1e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.奇函数,且对任意![]() ![]() |
B.奇函数,且存在![]() ![]() |
C.偶函数,且对任意![]() ![]() |
D.偶函数,且存在![]() ![]() |
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7 . 已知函数
.
(1)若
,
①求曲线
在点
处的切线方程;
②求证:函数
恰有一个零点;
(2)若
对
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd82845718b6b9f744deea1d9779c81.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
①求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea9824af71c9da5db5a00ec06063024.png)
②求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d29268e34e4cafff25f64b398a635786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49a5dd2066c68b2fb5f16731013cfc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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8 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f743bd3474bea3e10c9205970d7f934.png)
(1)求曲线
在点
处的切线方程;
(2)若
恒成立,求a的值;
(3)若
有两个不同的零点
,且
,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f743bd3474bea3e10c9205970d7f934.png)
(1)求曲线
![](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/9e9c599e8d420006448905acec2b8234.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50c66ed9ac7c9b79a030abf86895ccdb.png)
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名校
9 . 已知函数
,
.
(1)当
时,求曲线
在点
处的切线方程;
(2)当
时,求
的单调区间;
(3)在(2)的条件下,若对于任意
,不等式
成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799e0db4b64f85b168329f91554e1e0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)在(2)的条件下,若对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/998485ffeb46a0412ff1a0f814429257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11723704c1edf82bd3d5fdb2ad1ef93.png)
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2024-05-10更新
|
1016次组卷
|
5卷引用:北京市通州区2023-2024学年高三下学期二模数学试题
北京市通州区2023-2024学年高三下学期二模数学试题(已下线)【江苏专用】高二下学期期末模拟测试A卷(已下线)【人教A版(2019)】高二下学期期末模拟测试A卷云南省玉溪市通海一中、江川一中、易门一中三校2023-2024学年高二下学期六月联考数学试卷(已下线)核心考点3 导数的应用(恒成立,不等式,零点) B提升卷 (高二期末考试必考的10大核心考点)
名校
10 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)当
时,若曲线
在直线
的上方,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621148ed0a57848a6592e4f2f9fe40d1.png)
(1)当
![](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)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1d8d5cea065075fe50706abe3ae802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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