解题方法
1 . 已知
,函数
.
(1)若
,求
在点
处的切线方程;
(2)求证:
;
(3)若
为
的极值点,点
在圆
上.求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe45993e6bd636a4f34886bb3d72f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/788ebf70de03fb27efdb04252024b55a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd277b65fe7f9896b600a7950e57e47.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca84dff2367d3127e8ea7775981345b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/763f6c02b45500e5a42ce71f5e10ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 已知函数
.
(1)讨论函数
的单调性;
(2)若函数
的极大值为4,求实数
的值;
(3)在(2)的条件下,方程
存在两个不同的实数根
,
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16bd57d443b76da9c79f48791ce1ebec.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)在(2)的条件下,方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.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/3951a7bf1d9ca025aeef96c5c60411bd.png)
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2023-11-14更新
|
417次组卷
|
3卷引用:山东省青岛市第五十八中学2024届高三上学期阶段性调研测试(2)数学试题
解题方法
3 . 已知函数
在
处取得极值.
(1)求实数
的值;
(2)证明:对于任意的正整数
,不等式
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/349655426cff1798761e5aec1539c023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:对于任意的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67a89210cf3fda807166c5f03e9831b8.png)
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解题方法
4 . 已知函数
是R上的奇函数,当
时,
取得极值
.
(1)求
的单调区间和极大值;
(2)证明:对任意
,不等式
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03679d7dfb06bc2144bb16a702f4c5e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec54f53122364c46e1e43d1a84f210fd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05adfa1f46f8d2eb486991e61b727f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb9064ea9ead1b9363348096ca338c53.png)
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2022-09-23更新
|
1283次组卷
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7卷引用:山东省济宁市微山县第二中学2022-2023学年高三上学期第一次月考数学试题
名校
解题方法
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be49aca7bc043fac771c9b8bfe382672.png)
(1)求函数
的最大值;
(2)令
,若
既有极大值,又有极小值,求实数
的范围;
(3)求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be49aca7bc043fac771c9b8bfe382672.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/290587f506f21533da4dfcc8e5651930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec4e785fd0458bf1775629a888a2cf7.png)
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2020-12-03更新
|
934次组卷
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7卷引用:山东省实验中学2020-2021学年高三第二次诊断试题数学试题
解题方法
6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b428b94b55cb39156a53c626590e3761.png)
(1)若函数
在
处取得极值1,证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918b08f9c235e3ca66e9a07bfd2c369e.png)
(2)若
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b428b94b55cb39156a53c626590e3761.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c5db3528e1ca7fe75e1749409d7cb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918b08f9c235e3ca66e9a07bfd2c369e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee07b554d3fc2ab7a825ac859106422b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2020-04-21更新
|
955次组卷
|
3卷引用:2020届山东省泰安市高三模拟考试(一模)数学试题
名校
解题方法
7 . 已知函数
,
,
为自然对数的底数.
(1)若
,
,证明:当
时,
恒成立;
(2)若
,
,
在
上存在两个极值点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d1957e8d9112013651a9af6f212fda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b11fbec8ad9d116355022369d6aba9ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405dfcca25b76af059fb4c308983eae.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a783088120d67cc98936081e80fb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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8 . 已知函数
,
.
(1)若函数
有唯一的极小值点,求实数
的取值范围;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f53f81bca037a4383c1fab122a3cd3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4abdb0052a30184ec7bdc7e4fbd3922c.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e20fac1c42c7534c00ca6b37076f666a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16886b39748a0e4acba5d5822313012d.png)
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9 . 已知函数
有两个不同的极值点
.
(1)求实数
的取值范围;
(2)若
,求证:
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b4642ad1ec2a08a359762e3966212d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d98919b1335a8b7ca020636d1494ad0d.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ecdc6ff8e1a10a13d8e50a0881a9e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/023000c9506e47e89ce416a591cc8f10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96b51949dcfff981d7e8af501a637ba.png)
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名校
10 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83f7df08f25a779eca8c219d8a3dba2c.png)
(1)若
,证明:
;
(2)若
在
上有两个极值点,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83f7df08f25a779eca8c219d8a3dba2c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbfe8e7fb253685e0e50bae0c5482314.png)
您最近一年使用:0次
2019-12-26更新
|
1306次组卷
|
7卷引用:山东省实验中学2021-2022学年高三上学期第二次诊断考试数学试题
山东省实验中学2021-2022学年高三上学期第二次诊断考试数学试题2019年12月河北省沧州市普通高中高三上学期教学质量监测理科数学辽宁省锦州市渤大附中、育明高中2020-2021学年高三上学期第一次联考数学试题(已下线)专题03 利用导数解不等式与不等式恒成立问题(讲)--第一篇 热点、难点突破篇-《2022年高考数学二轮复习讲练测(新高考·全国卷)》(已下线)专题13 利用导数解决函数的极值、最值-学会解题之高三数学万能解题模板【2022版】江苏省南通市2023-2024学年高三上学期期初质量监测数学试题江西省宜春市宜丰中学创新部2024届高三上学期第一次(10月)月考数学试题