解题方法
1 . 已知
,
,
,其中e是自然对数的底数,
.
(1)讨论当a=1时,函数
的单调性和极值;
(2)求证:在(1)的条件下
;
(3)是否存在正实数a,使
的最小值是3?若存在,求出a的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d0ff7ac083b888d0055e49bf130a6e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3980c52927f12c114f3b291ad714d778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc6deca979f50c3310464cca848768a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5f7f23e7f20dd8bc65a4967cd306782.png)
(1)讨论当a=1时,函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:在(1)的条件下
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf67014ab217c6cacd76dc4b19774d8.png)
(3)是否存在正实数a,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2 . 关于函数
,下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d42bc1614c3372edf362b4c07154fba.png)
A.![]() ![]() |
B.函数![]() |
C.存在正整数![]() ![]() |
D.对任意两个正实数![]() ![]() ![]() ![]() |
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3 . 已知函数
.
(1)若
,讨论函数
的单调性;
(2)当
且
时,
的极大值为M,
的极小值为N,求
的取值范围.(参考数据:
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d5c04ff5fc31610f421561dc6f553c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f9560f8f90d4addcf5fb6fdcc7956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc91d92eb161e54def20b039d2089201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd2137457b0901a29711ecf0a93eaf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12a76edbb3e98e3ff41c03401769d1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50101047632b94dcd5cf8035b093cc5.png)
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解题方法
4 . 已知函数
,其中a,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d285a4c557fc9748105b62ccd94b7859.png)
(1)若
在
处的切线方程为
,求
;
(2)若
,
①当
时,求
的单调区间和极值;
②当
恒成立时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a814f85dea375207f54904fc89332725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d285a4c557fc9748105b62ccd94b7859.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df9b4ac1458224ff0cd58a9118a725c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0985b973395bcd371cd1e26d3fcd1c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/429d963721ba73f4233eb0426e8a1823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f84a3ecb5b162a65745b3657ce0d957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2021-11-23更新
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2卷引用:四川省遂宁市2021-2022学年高三上学期零诊考试数学(理科)试题
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解题方法
5 . 已知函数
,
,
,令
.
(1)当
时,求函数
的单调区间及极值;
(2)若关于
的不等式
恒成立,求整数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b90c5d5a2ae54f6186ab53d39083fdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa0b6d7f1f1157896b16bff2743a1b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71607511fdd4faa9e832345ceb2a817d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8493a0cd10d3d0399173c04163740a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2531067066de05b735ce7cd541101e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2021-10-26更新
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3卷引用:四川省南充市白塔中学2020-2021学年高三下学期第九次诊断性测试数学(理)试题
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解题方法
6 . 已知函数
.
(1)求
的极值;
(2)已知
,且
对任意的
恒成立,求
的最大值;
(3)设
的零点为
,当
,
,且
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b276d8b7113c704d6a063a45a27dc334.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835705ff91d278fa24e760473864257b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/908cba2b3eeb3728b003144fedd4c571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c7ec96e9bf06fe5e93edbe8b6901ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884ce1e9436d39f34f6d3116cb2a140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/440b4409f9eeed6c8dbcbe2c6aa82186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2210f152080d9a68a97c805f5c1cde96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dcc2e7dee9cdc0b781c66a74727af2a.png)
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7 . 已知函数
,
.
(1)求
在
的极值;
(2)证明:
在
有且只有两个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc873fc03e6e4d3c4ba02f8b1147b20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d9d46d6ec64d1b923a9f8ec789991dd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ff8dca35b759d3051b62badd7d76bc.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa662f0273f0921c1fa4727f632395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a7792efd7f82bfa7549db4cb6ca761.png)
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6卷引用:四川省自贡市2021届高三三模数学(理)试题
四川省自贡市2021届高三三模数学(理)试题四川省自贡市2021届高三三模数学(文)试题江西省南昌市豫章中学2022届高三入学调研(B)数学(文)试题(已下线)考点12 导数的应用-备战2022年高考数学(文)一轮复习考点帮(已下线)4.6 导数的综合运用(精讲)-【一隅三反】2022年高考数学一轮复习(新高考地区专用)(已下线)第14讲 零点问题之取点技巧-突破2022年新高考数学导数压轴解答题精选精练
解题方法
8 . 已知
,其中
.
(1)当
时,求
的极值;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a836d0f5603f546b2b6aa11a0760b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6e2c9f63b1e6638a09d121d05176741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
9 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381b69ad35655efe1a9b67a1a32429ac.png)
(1)若函数
在区间
内是增函数,求实数
的取值范围;
(2)当
时,证明:函数
有极大值(记为
), 且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381b69ad35655efe1a9b67a1a32429ac.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3908ad61f1cea086545c613eb01d22d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dc56a349930f604e748c531922c4c52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfee5b708320df678394f46ce5542b6.png)
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10 . 设函数
(
).
(1)若
,求
的极值;
(2)讨论函数
的单调性;
(3)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b00e2f511c216c0ba76956aeaffac5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b60682e4d65aff48172f98ba1a4866d.png)
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2020-12-31更新
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9卷引用:四川省凉山州2021届高三一模数学(理)试题