名校
解题方法
1 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4fce8955baad2043f4ffdb3aca85335.png)
(1)当
时,求
的单调区间;
(2)当
,
时,函数
的两个极值点是
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
,点
,
的斜率为
,若
恒成立,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4fce8955baad2043f4ffdb3aca85335.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebc20d351d51723c9b0a07a20ac14114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dafa6cf5b9002d734b287e7983ee7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.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/3fa469ee3afe776064657b3551aedfe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e79c6266364361b8d5bc1bd3e1f060.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4780e880f3d80d57005fc6c69e5f428.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95cefb160c373407a49e3a8aee1a228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8940a38b96de9a01fc0f6ef17753cf21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
解题方法
2 . 已知函数
,
,若满足
恒成立,则实数
的取值范围是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e176324a7b57b4176f4e6fb97c63b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97148e04ca6a9f9dca0aba91ce4e1d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7b996c762c76891ffdff5add704550c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 若函数
有两个零点,则实数
的取值范围是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0ea8a55ea09483acce9502da3fda34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 设函数
.
(1)当
时,讨论函数
的单调性;
(2)若对任意
及任意
,恒有
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad62965f84650bca6f230d5f19b1d92.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05cac8a8949fae95b195425ce890947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4169c5f606352788872a03fe5476fea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b5d191f100c1d53b695aef1367ae817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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5 . 已知函数
的定义域为
,部分对应值如表:
的导函数
的图象如图所示,下列关于函数
的命题
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/112854e4-642e-48d0-9b23-438bd5d26127.png?resizew=166)
①函数
的值域为
;
②函数
在
上是减函数;
③如果当
时,
的最大值是2,那么
的最大值为4;
④若函数
有4个零点,则
.
其中真命题是___________ (只须填上序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0581fcaa2dcf917479091fded7f5b21b.png)
x | ![]() | 0 | 4 | 5 |
![]() | 1 | 2 | 2 | 1 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/112854e4-642e-48d0-9b23-438bd5d26127.png?resizew=166)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
③如果当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7924069f67dcce50ae8f3bdef13f8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
④若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcefa1eadaa807e3fe6c61a2f8d2dea9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d4a2d4a99bf35ab3fefbdf9a442df2d.png)
其中真命题是
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2021-08-11更新
|
171次组卷
|
2卷引用:四川省遂宁市射洪市射洪中学校2020-2021学年高二下学期期中数学理科试题
名校
解题方法
6 . 设函数
,
.
(1)当a=b=1时,若
恒成立,求m的取值范围.
(2)设
有两个零点
,且
成等差数列,试探究
值的符号.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df9a16664ad088899f6437b9637b80b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f31e627455629733c86d8372e529bf4.png)
(1)当a=b=1时,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03cb579aedb944a49293e97367a43f5f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f518f7668f0191eb0d7aaf74fe5893c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be07753eab86fa9c439a65db51c9a9e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dad26123e6a3f4bd2857ec6ac7f9dfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f210cdd2d4374950f4ef1835c47002f1.png)
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名校
解题方法
7 . 已知函数
,若存在实数a使得
恒成立,则实数m的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c491d80d833bab54cde3deb341a29a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e520c1ab44faaa476a5f3f6181db0f4.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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8 . 函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6615f59575a76ac534adfe0e5a415671.png)
有两个不同的零点,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6615f59575a76ac534adfe0e5a415671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c235ca725ade5c8b07943ac106a90fb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 已知函数
.
(1)求函数
的极值点;
(2)设
,若在
上至少存在一个
,使得
成立,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46ce8278a0c69d0dd8966709358bec88.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7555fac1d8eaee8a92cb2f7c60baadd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0b6ca237b90b49a91d9d74d007efdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f97db80e5bf3c061776dc9008d2f2c7d.png)
您最近一年使用:0次
2021-08-07更新
|
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2卷引用:四川省仁寿第一中学校南校区2020-2021学年高二第三次质量检测(6月月考)数学(理)试题
名校
10 . 若函数
存在零点,则a的取值范围为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972a3109c9527b28c149e87ae4b57d8f.png)
您最近一年使用:0次
2021-08-07更新
|
305次组卷
|
4卷引用:四川省仁寿第一中学校南校区2020-2021学年高二第三次质量检测(6月月考)数学(理)试题