1 . 已知函数
是定义域为
的偶函数,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c69303bd9eccb3ccb55c9e4cd03a8a3.png)
______ .
是
的导函数,若对任意
,使
成立,则不等式
的解集为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105068fe440b555880e9c566e6fd3f5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57457379efecec3a8f98377bc5c65d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c69303bd9eccb3ccb55c9e4cd03a8a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b77b740391108ac5e4d36461efac4578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc59b5d33285b96b0cc21094aaa18572.png)
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2 . 若
,都有
成立,则实数
的取值范围是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa2686060312ed2221ad9de62c260c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31d39e253f2da686e7e589857bb23117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-04-10更新
|
507次组卷
|
2卷引用:第十四届高二试题(B卷)-“枫叶新希望杯”全国数学大赛真题解析(高中版)
3 . 已知函数
有两个零点,则实数
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e93aa746ec436ef3f412fb65f14401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 已知
,则
的大小关系是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fcb030e14770eae4d232255bb70e530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
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5 .
,函数
没有极值的充要条件为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62f5fac99ec501d2f2570de8c8e546f4.png)
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6 . 已知函数
既是二次函数又是幂函数,函数
的图象与函数
的图象关于直线
对称.若直线
与函数
的图象和函数
的图象的交点分别为
,
,则当
达到最小时,
的值为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a76db9d90c057be5b5eb8727bd08979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
A.1 | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-03-20更新
|
114次组卷
|
3卷引用:第十二届高二试题(A卷)-“枫叶新希望杯”全国数学大赛真题解析(高中版)
7 . 已知定义在R上的函数
(
是
的导数),
且
,则
的值______ .(在“小于零、等于零、大于零”中选一个填上)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17d45142992583fe75c4d000d7355450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a60854623ecdd7d47e8e119594e41c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86a229b88f0c9a1fa3fccd43e1c0521e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1320af3e28fea8c6414b1381adaf5e52.png)
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解题方法
8 . 已知函数
,则不等式
的解集为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7917130051de29c1f33dedbf5773c7b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
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9 . 设函数
,且
,则当
时,
的导函数
的极小值为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd62d9969adba7f42d582ccab479cde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96effbf356f5ad5594152169ad7ccc92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
A.2 | B.3 | C.4 | D.5 |
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10 . 已知函数
.
(1)当
时,求函数
在
处的切线方程;
(2)求函数
的单调区间;
(3)若函数
有两个极值点
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e09674ee7c047c9c36f9743359387a7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1f9fa86fe5015298d7ef9f51cc31207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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