2024高三·全国·专题练习
解题方法
1 . 已知函数
.
(1)若函数
有三个零点分别为
,
,
,且
,
,求函数
的单调区间;
(2)若
,
,证明:函数
在区间
内一定有极值点;
(3)在(2)的条件下,若函数
的两个极值点之间的距离不小于
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077315c5a7b12294497294e536831d77.png)
(1)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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f5cd91996571c9da95e6f26bc80661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23292eca257af6a97309ee40ce6cbf9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37f19a2ad8f24cf63bff68be15faa67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799f6009a476fa056e1af71f26dd2fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094cba781181aeb90752170e9ba6c94.png)
(3)在(2)的条件下,若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
您最近一年使用:0次
2 . 定义:若曲线
或函数
的图象上的两个不同点处的切线互相重合,则称该切线为曲线
或函数
的图象的“自公切线”.
(1)设曲线C:
,在直角坐标系中作出曲线C的图象,并判断C是否存在“自公切线”?(给出结论即可,不必说明理由)
时,函数
不存在“自公切线”;
(3)证明:当
,
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0ee1a614e16f3092d318d74a252775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e78b9c2b82517c887804b6ad8742a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0ee1a614e16f3092d318d74a252775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e78b9c2b82517c887804b6ad8742a85.png)
(1)设曲线C:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda51f0c169b59ac826994bebae3bc6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88a033e1ff47a23c84900de3c27ef453.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655c46b33730f3a29b9ec3024df71375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6725fd6db412e3c0caf9987018b43994.png)
您最近一年使用:0次
2024-05-30更新
|
437次组卷
|
2卷引用:辽宁省大连市二十四中学2023-2024学年下学期高三第五次模拟考试数学卷数学
名校
解题方法
3 . 已知函数
.
(1)当
时,求
在
处的切线方程;
(2)若函数
在
上单调递增,求实数
的取值范围;
(3)求证:
.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662704fdd021f1cc3c239cb0362b4017.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5915d15cfa8ee93afb9628d2a98d88b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d927d40b4ea833a1423554a3e3fcbf8.png)
您最近一年使用:0次
名校
解题方法
4 . 已知函数
.
(1)若
恒成立,求a的取值范围;
(2)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f732e2a644b6c0fc9741868d3721fd7b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a600d7d8138a9179410797b0cb24810.png)
您最近一年使用:0次
2024-04-10更新
|
1612次组卷
|
3卷引用:辽宁省大连市2024届高三下学期第一次模拟考试数学试卷
名校
5 . 已知函数
,若对任意实数
,都有
,则实数
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9538f6b25c6c6bd0810696386939e75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd85d4af7dfca7633dd9ca7993ec4d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d874f5810ed3dace9240a02dc7cbf094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-04-06更新
|
298次组卷
|
2卷引用:辽宁省大连育明高级中学2023-2024学年高二下学期期中考试数学试卷
名校
6 . 记函数
在
上的导函数为
,若
(其中
)恒成立,则称
在
上具有性质
.
(1)判断函数
(
且
)在区间
上是否具有性质
?并说明理由;
(2)设
均为实常数,若奇函数
在
处取得极值,是否存在实数
,使得
在区间
上具有性质
?若存在,求出
的取值范围;若不存在,请说明理由;
(3)设
且
,对于任意的
,不等式
成立,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95cf3765e5650555113994da8771e3e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0c99ddd028f0bc3b1d64924ff0f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df0dd6144e9a30d1a063b690033c3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca214aa6276b96d67a451c3fdbc59b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca02970d65fea8d2e9dab7dc060f073f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1416d4381e78902b45e34142529a8a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc7c3763c1078093d2f3da4368100fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232d1ce3ad14256b1543e6007ff1675d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b85b26594fd953a8154c49948ca88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2024-03-29更新
|
776次组卷
|
4卷引用:辽宁省大连育明高级中学2023-2024学年高二下学期期中考试数学试卷
名校
7 . 已知函数
在
上可导且
,其导函数
满足:
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33875cdd9542d54912febef6b02d014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281bb4da5c83fd6c6f95bd1d30524600.png)
A.函数![]() |
B.函数![]() |
C.当![]() ![]() |
D.![]() ![]() ![]() |
您最近一年使用:0次
2024-02-08更新
|
1379次组卷
|
5卷引用:辽宁省大连育明高级中学2023-2024学年高二下学期期中考试数学试卷
辽宁省大连育明高级中学2023-2024学年高二下学期期中考试数学试卷山西省临汾市2024届高考考前适应性训练考试(一)数学试题(已下线)信息必刷卷01(已下线)模块2 专题3 构造函数 解不等式练(高考真题素材库之典型好题母题)(已下线)信息必刷卷04(江苏专用,2024新题型)
名校
8 . 设
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eff1003e9744f3cf7dc0c9c1ea92267.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-01-16更新
|
2568次组卷
|
6卷引用:辽宁省大连市2024届高三上学期双基测试数学试题
辽宁省大连市2024届高三上学期双基测试数学试题(已下线)广东省深圳市深圳中学2024届高三一月阶段测试数学试题(已下线)专题10 导数12种常见考法归类(2)江苏省四校联合2024届高三新题型适应性考试数学试题(已下线)新题型01 新高考新结构二十一大考点汇总-1湖南省衡阳市第八中学2024届高三下学期适应考试数学试题
2023·全国·模拟预测
名校
9 . 已知函数
,若
对于
恒成立,则实数
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f891aa5085a14034f792d741e70e443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb5140d9bfefa0fc1f6d428ff5c2b485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e82c4003d20b36777f7aea584e3dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
10 . 已知函数
.
(1)若对
时,
,求正实数
的最大值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdfd509af00960319b088b20d3d4189a.png)
(1)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b705b0958495774d529c2e2a6c3ae94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/477b45c90cd1fd5bd772d5b93e1c7508.png)
您最近一年使用:0次