名校
解题方法
1 . 已知函数
.
(1)若
对
恒成立,求
的取值范围;
(2)当
时,若关于
的方程
有三个不相等的实数根
,
,
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139ccda5ac5ed8c01bd0e87e84d30e09.png)
,求
的取值范围,并证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25af1b7613f714301020bb09a33d8fe8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427ddc261e4aea13a25fa479749f4074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e82c4003d20b36777f7aea584e3dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c5f6fe92b97f07fb31b118fa97b11a.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/139ccda5ac5ed8c01bd0e87e84d30e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ebb401767499a3b5eedf56cb36b4127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9e12d9f9b1dbd7a1ad8fffe752f5e7.png)
您最近一年使用:0次
2024-05-22更新
|
218次组卷
|
2卷引用:甘肃省武威第六中学2023-2024学年高三下学期第五次诊断数学试卷
2 . 对于三次函数
.定义:①
的导数为
,
的导数为
,若方程
有实数解
,则称点
为函数
的“拐点”;②设
为常数,若定义在
上的函数
对于定义域内的一切实数
,都有
恒成立,则函数
的图象关于点
对称.
(1)已知
,求函数
的“拐点”
的坐标;
(2)检验(1)中的函数
的图象是否关于“拐点”
对称.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012429b7101ba0f84e7b45598ed12db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1fa6ca9eb7cea9131dad36db6a0ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abde3621d19a60d8b0cad42c06d8891.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d5f97843013ef486e10f66543562a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)检验(1)中的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
名校
解题方法
3 . 已知
,则下列不等式正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d229cbec798c9c278a9b5979cb38247.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-05-19更新
|
914次组卷
|
4卷引用:甘肃省天水市第一中学2023-2024学年高二下学期第二学段检测考试(6月)数学试题
甘肃省天水市第一中学2023-2024学年高二下学期第二学段检测考试(6月)数学试题湖北省宜荆荆随恩2024届高三5月联考(二模)数学试题(已下线)5.3.2函数的极值与最大(小)值(3)(已下线)第三章 第二节 导数与函数的单调性【同步课时】提升卷
名校
解题方法
4 . 对于函数
,下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f53f81bca037a4383c1fab122a3cd3d.png)
A.![]() ![]() ![]() | B.![]() |
C.![]() | D.若![]() ![]() ![]() |
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名校
5 . 设函数
.函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f882bab36375f68538d58fb58f826f.png)
(1)当
时,判断函数
的零点个数;
(2)令函数
,求函数
的单调区间;
(3)已知函数
在
处取得极大值,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cfae7cd94ca57c89308f51484d934af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f882bab36375f68538d58fb58f826f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c712829d60b4ea93966a5c68c24d677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0dab303a35550de0da3433053c5b14.png)
(2)令函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aa647d4d259e2f7c65ee2b7be82726e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
6 . 已知函数
是自然对数的底数.
(1)若
,证明:
;
(2)若关于
的方程
有两个不相等的实根,求
的取值范围;
(3)若
为整数,且当
时,不等式
恒成立,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d6b43fc556c4b205abba37fc4a0dc9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5967cc62862986840af4dd29df4bcc41.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa757c82f454fe33f592264a7e4d08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04391464f10c513e23be28dc5eeff88e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d347d5b8729ddc0417eb8eb0a13c7218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
7 . 函数
(其中
为自然常数).则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33427bd6641954f6e4deab695e815b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ab625f9a61f620b0c59920729c52c37.png)
A.![]() ![]() |
B.![]() ![]() ![]() |
C.![]() ![]() |
D.![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
8 . 某商户销售
、
两种小商品,当投资额为
千元时,在销售
、
商品中所获收益分别为
千元与
千元,其中
,如果该商户准备共投入5千元销售
、
两种小商品,为使总收益最大,则
商品需投入______ 千元
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5727d16e86c5af5ddd1b23daa3dc636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9224bb9bd499e07e5e8a8100d0a4c0fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
名校
解题方法
9 . 已知函数
.
(1)求函数
的极值;
(2)若对任意
,都有
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b491d82ef8cc6440ecf9c30ff89bf4d2.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48350c9f896c18a64f27867ca81c9be2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2942e2647554b44127bfce7b22f36a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-05-12更新
|
784次组卷
|
4卷引用:甘肃省酒泉市2024届高三第三次诊断考试(5月)数学试题
甘肃省酒泉市2024届高三第三次诊断考试(5月)数学试题河南省许昌市魏都区许昌高级中学2024届高三下学期5月月考数学试题安徽省合肥市一六八中学2024届高三下学期最后一练数学试题(已下线)重难点突破05 利用导数研究恒(能)成立问题(十一大题型)-2
10 . 已知3是函数
的极小值点.
(1)求
的值;
(2)若
,且
有3个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99aa855128ded58e5ee664733051edd7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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