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1 . 已知函数
.
(1)讨论函数
的单调性;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e711ad73e9a501b2eced5946d77a1af.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba77024a68f858c6f391e835b4f7ed0.png)
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2022-12-19更新
|
525次组卷
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2卷引用:江苏省徐州市2022-2023学年高三上学期期末模拟数学试题
2 . 已知
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d37ba212e5122d0fd1d25dda67f0de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45b4665d35920b7af8f78e86d9cd85f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e970bb8905907745672b55f43f35c047.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
3 . 设
,函数
.
(1)求证:
存在唯一零点
;
(2)在(1)的结论下,若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2b3a457ebfd6e86ae30219f4bc45a44.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)在(1)的结论下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76fcbdf2921f8918880ed58166039993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0277dc483305886d6a1ce0833634713f.png)
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2022-12-03更新
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614次组卷
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4卷引用:江苏省苏州八校联盟2022-2023学年高三上学期第二次适应性检测数学试题
江苏省苏州八校联盟2022-2023学年高三上学期第二次适应性检测数学试题江苏省连云港市赣榆高级中学2022-2023学年高三上学期12月学情检测数学试题(已下线)5.3 导数在研究函数中的应用(练习)-高二数学同步精品课堂(苏教版2019选择性必修第一册)广东省汕头市潮阳实验学校2024届高三上学期元月阶段测试数学试题
4 . 已知函数
.
(1)讨论函数
的单调性;
(2)设
,
是函数
的两个零点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf349263bf8a6bfec0a91d10f1151a2.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/546a1ee9369c1c238e3e9ff1bb4a236e.png)
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解题方法
5 . 已知函数
,
且
存在极值
.
(1)求
的取值范围;
(2)若存在
使得
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797ea99522cd6d194d20b881ff58fe64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c342e9a6f6dfb90e2863ab537c3fd382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6999cc41d0de41c4114f4adda1952ca.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f58d4591d668b4bc32fae4faab8298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859458471c86ae39e0cc42d2d960d03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/757144a9fbcf27dd4fe14e17d50388e6.png)
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2022-11-10更新
|
637次组卷
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3卷引用:江苏省南通市海门市2022-2023学年高三上学期期中数学试题
江苏省南通市海门市2022-2023学年高三上学期期中数学试题(已下线)第九章 导数与三角函数的联袂 专题四 利用导数证明含三角函数的不等式 微点2 利用导数证明含三角函数的不等式(二)江西省贵溪市实验中学2024届高三上学期新高考模拟检测(三)数学试题
名校
解题方法
6 . 已知
,
.
(1)若存在
,使
成立,求实数a的取值范围;
(2)是否存在实数a,使
对任意
恒成立?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc481a476572a65e4adb83d4974eefed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1b2c980f19ed470eb8abcc9e80d8219.png)
(1)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef0d07828e157417eecfd10aad5e67a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f23ea1f2cea3ed4f92697ff319bfb6.png)
(2)是否存在实数a,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4979dfbddd3f7055ddb3d35cb711f44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416540999fe61429b46a20181ab4ce1a.png)
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解题方法
7 . 已知函数
,
,
(1)若
在
存在极小值点,求
的取值范围;
(2)若函数
有3个零点
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ec13d0c7a2f811a742d7e89960c5fec.png)
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63058af7d2cebd31923695c202b5f1f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dba7294809f75ea3ac666b709f71b4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/848c33e3506416358d9f0d3ee66f67a9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65356f586eea8b1a0e18b0c1ee107852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ff16773bd63036c8c881d8417ab555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3551ac437add8a9d19e141adf9e9df0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12a4eecd249473a831d0ee472470240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9565876bc50bceb63e5793c8c67a9032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ec13d0c7a2f811a742d7e89960c5fec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0803dd245899395055f60be4c435034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8adbad2beab443a8607d6ac9215daf.png)
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2022-10-18更新
|
562次组卷
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2卷引用:江苏省南通市海安高级中学2022-2023学年高三上学期第二次月考数学试题
22-23高三上·江苏盐城·阶段练习
名校
8 . 已知函数
:
(1)讨论
的单调性;
(2)设
,若
在
,
处的切线过点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98b956e8f03bef528ac4d3f3d118d29f.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23204c7ce89219fd16a0c6e01f5ee8cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362e7bee16baef0eec7fb661717e1f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36c639bebbd313bd594b9c56d314738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31b2f4e61685e716a9ce91b939e10032.png)
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22-23高三上·江苏盐城·阶段练习
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解题方法
9 . 设正实数
,
满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2fdeba282b028321696be7f90f2cbfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddc31fbb39a048ff31af6179a3d74153.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 已知函数
.
(1)当
时,讨论
的单调性
(2)证明:
有唯一极值点t,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0571f1bbd6076e20c9cd91c9b777b425.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81ed7f6a4475e0fa682fa81ee747da3.png)
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