1 . 已知函数
,
.
(1)讨论
的单调性;
(2)若
有两个零点,求实数
的取值范围;
(3)若
对任意的
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eaa6d55cdb24cff59f22f8a09b27160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026d50aeb347823e800aa11442b80331.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780876acd6f251de9b8510f4def91b5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
昨日更新
|
815次组卷
|
4卷引用:辽宁省辽阳市辽阳县辽阳石油化纤公司高级中学2024届高三下学期模拟考试数学试题
2 . 已知函数
.
(1)求函数
的单调区间;
(2)若
,求函数
在区间
上的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b527fccc73edf11c0282eb2a67918dc.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d85e1973130da5abb1461be6b3690550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0dfcda9ae3994fc00ad787935d8475.png)
您最近一年使用:0次
3 . 已知函数
,定义域为
.
(1)讨论
的单调性;
(2)求当函数
有且只有一个零点时,
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b524c2fcb094954f09626b08536ef1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求当函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-06-11更新
|
687次组卷
|
2卷引用:辽宁省沈阳铁路实验中学2024届高三第八次模拟考试数学试题
名校
解题方法
4 . 已知函数
.
(1)求函数
的最小值;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ae309841b3cffa828d8b1537f6ed81.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c7914c666a4e4dc6a0ff76f01c47d6.png)
您最近一年使用:0次
5 . 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
|
434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
解题方法
6 . 已知函数
,其在
处的切线斜率为
.
(1)求
的值;
(2)若点
在函数
的图象上,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c074042b84baa341258b1e701e1aea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d437fc0f48ceb7b5b9bcef34e3448c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64d924836b4292239d9726c6473d7f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86eb59d57b46c345081ecf1317f5f27c.png)
您最近一年使用:0次
7 . 设函数
的定义域为I,若
,曲线
在
处的切线l与曲线
有n个公共点,则称
为函数
的“n度点”,切线l为一条“n度切线”.
(1)判断点
是否为函数
的“2度点”,说明理由;
(2)设函数
.
①直线
是函数
的一条“1度切线”,求a的值;
②若
,求函数
的“1度点”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b359345c5afa1739bf5ebf8982e1d959.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f16fb94e679867d1aeab1b81a9765a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
(1)判断点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b969fe0f970a6605c114953c88d9d71e.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b7742abf1c609b8a4cc5c2dcc05814.png)
①直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0e212cdbfba6610bc55df2c1a737407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
您最近一年使用:0次
名校
8 . 已知函数
.
(1)若
,求曲线
在点
处的切线方程;
(2)若
,试讨论
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08c175efdda7cf6dd5d113ce98bfa8d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3897bf276a0b6c2121917d39b369df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c7d6a607085cd85bea646a11243cc3c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a967d4c78e4d658d1fd4afb33c3ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
您最近一年使用:0次
2024-05-20更新
|
1408次组卷
|
5卷引用:辽宁省抚顺市六校协作体2024届高三下学期5月模拟考试数学试卷
9 . 已知函数
,(
,
).
(1)讨论函数
的单调性;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1139dccb9e35e41b750bf66b4e996330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4dc334f806ac8924be42bbded1b885a.png)
您最近一年使用:0次
解题方法
10 . 已知质数
,且曲线
在点
处的切线方程为
.
(1)求m的值;
(2)证明:对一切
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e2da4647a9925ccc924b0f9f3b40ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea9824af71c9da5db5a00ec06063024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8eb06f527d4201b93636710c62d461.png)
(1)求m的值;
(2)证明:对一切
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92222bd1bfa79c6082eea07ced5a98ef.png)
您最近一年使用:0次
2024-05-14更新
|
465次组卷
|
2卷引用:辽宁省葫芦岛市协作校2023-2024学年高三下学期第一次考试数学试卷