解题方法
1 . 已知函数
,其中
为实数.
(1)当
时,
①求函数
的图象在
(
为自然对数的底数)处的切线方程;
②若对任意的
,均有
,则称
为
在区间
上的下界函数,
为
在区间
上的上界函数.若
,且
为
在
上的下界函数,求实数
的取值范围.
(2)当
时,若
,
,且
,设
,
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4d96931977f6f5462acb196bcd417e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
①求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187c21027ff08411931d32c530b64fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
②若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea4d74f476f741b75a448ee01c0e86c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0f121036d30c000b01b7be98d9c8a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0f121036d30c000b01b7be98d9c8a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e75907a1b513cdf63614b4b68ece89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdb0aa7bf71da74a9b3d4a022812290a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f861459b5e5a3ce298f205d9677e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dd34bc2979bfed0fa99269635dde578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9499b9c4b5292d3f28799d1e96653ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/253fe46f6392ea2a63475453fbe5b16d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8cce18618decec25cc47f40f2f7478f.png)
您最近一年使用:0次
2 . 已知函数
若函数
(
)(
为自然对数的底数)恰有4个零点,则
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfb4e3b94f9d57e0a137fcb770f3e5f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c57a713236f811d406014d1b9d7d1092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36b234ba460321e811de1729eadd4b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
解题方法
3 . 已知函数
(
),
.
(1)求函数的极值;
(2)若
对任意的
恒成立,求实数
的取值范围;
(3)求证:
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb0efa793fc95d2bbcc8eec1d375343f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c9e984f50dac827078864092aa9a7bc.png)
(1)求函数的极值;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5822ea5f9009e579f59f011db39196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5816f5a4a74bbf091588680f9885b829.png)
您最近一年使用:0次
4 . 已知函数
,
,
.
(1)判断
是否对
恒成立,并给出理由;
(2)证明:
①当
时,
;
②当
,
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea987f231a61367682b6abb1d490860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c7743ab916fb33ca0d2fc597cfc672f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e653994b245fbdc2ac3458429c65e69e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3add1679c27392a1a7f635723a4b36eb.png)
(2)证明:
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d005e2d92072f3ed9289c5bb80f55cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5494b7905201c6f627c12b85b8a369.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c8b04a43f618f95b4ad5474944a64c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd436cb785ccb4d29baa6bf70c10a09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6495c0fcf9672516f5cb8c5ef614df13.png)
您最近一年使用:0次
2024-03-12更新
|
1302次组卷
|
8卷引用:天津市滨海新区塘沽第一中学等十二校2023-2024学年高三下学期二模考前模拟考试数学试卷
名校
5 . 已知函数
,
,
.
(1)设
,试讨论函数
的单调性;
(2)若
对于定义域内的任意
恒成立,求实数
的取值范围
(3)设
,对于任意的
,总存在
,使不等式
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/153a430f99c4004a94325ab49d84dc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f049a5f960728c60a909821b2404b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568041d6adb0ccc31892181f6206afd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29836991ef5eb74372a6827f5810d7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9122b0871365ec49002a62401ac7f693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fae35542c8e8114f3cfc05b400ba565.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ad23d93c0e20425a3a7f3a8605a61d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6319c453a96a1a75d46aaf4b51ede08f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
6 . 已知函数
,
且
.
(1)当
时,求曲线
在
处的切线方程;
(2)若
,且
存在三个零点
,
,
.
(i)求实数
的取值范围;
(ii)设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd34ef1116ad10637283e654cacb2b31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.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)
(i)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7803d86067299198e6d14b0c83947f58.png)
您最近一年使用:0次
2023-11-30更新
|
707次组卷
|
3卷引用:天津市滨海新区塘沽第一中学2024届高三毕业班八校联考数学模拟试题
名校
7 . 已知函数
.
(1)讨论
的单调性;
(2)证明当
时
;
(3)若
有两个零点
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8956a9ff94ca6602eff6f448557ca903.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394ce29446a32bc73fb4e99320c22a25.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd888afdcfdb3e91a157d50f65e915e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff3714eb626830b60b6f8fd133b42993.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
,
.
(1)当
时,
(i)求曲线
在点
处的切线方程;
(ii)求
的单调区间及在区间
上的最值;
(2)若对
,
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c589325db8016e1566cdcf20d43e288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111324440f372e35f0f37dd29837bea7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
(i)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea9824af71c9da5db5a00ec06063024.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f909328384f9c52134243753d9c954ef.png)
(2)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735fe7737e87152893863b1a11f7a197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0527a896aec4a245945e5edee00deed.png)
您最近一年使用:0次
2023-09-16更新
|
744次组卷
|
4卷引用:天津市滨海新区塘沽第一中学2024届高三上学期第一次月考数学复习卷5
名校
9 . 已知函数
,
(1)当
时,求函数
在
处的切线方程;
(2)讨论函数
的单调性;
(3)当函数
有两个极值点
且
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5facb7583ea00e6d8db952d80557f4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)当
![](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/9b384412acba251d87902ab928902f16.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b314f6ccb0a3e4fc15685d85e55bf6.png)
您最近一年使用:0次
2023-09-05更新
|
651次组卷
|
14卷引用:天津市滨海新区塘沽第一中学2024届高三上学期第一次月考数学复习卷2
天津市滨海新区塘沽第一中学2024届高三上学期第一次月考数学复习卷2福建省宁化第一中学2022届高三9月第二次月考数学试题广东省梅州市东山中学2022届高三上学期期中数学试题天津市第五十五中学2021-2022学年高三上学期10月学情调研数学试题云南衡水实验中学2022届高三上学期期中考试数学(理)试题黑龙江省哈尔滨工业大学附属中学校2021-2022学年高二上学期期末考试数学(理)试题(已下线)2020年高考天津数学高考真题变式题16-20题(已下线)第13讲 双变量问题-2022年新高考数学二轮专题突破精练河南省洛阳市洛宁县第一高级中学2022-2023学年高二下学期2月月考数学理科试题江苏省南京大学附属中学2022-2023学年高二下学期3月月考数学试题广西壮族自治区梧州市苍梧中学2022-2023学年高二下学期3月月考数学试题天津市五区县重点校2022-2023学年高二下学期期中联考数学试题(已下线)模块五 专题5 期中重组卷(广东)(已下线)导数专题:导数与不等式成立问题(6大题型)-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第二册)
名校
10 . 已知函数
,
.
(1)若
,求m的值及函数
的极值;
(2)讨论函数
的单调性:
(3)若对定义域内的任意x,都有
恒成立,求整数m的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8dce6087f50dacf34591f7520132f89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8d1a34435611f6a59eac3dbfeb6e17.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70dfd3b70aab0849a459a241d904aa73.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)若对定义域内的任意x,都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
您最近一年使用:0次
2023-07-14更新
|
1815次组卷
|
6卷引用:天津市滨海新区2022-2023学年高二下学期期末数学试题
天津市滨海新区2022-2023学年高二下学期期末数学试题(已下线)第二章 导数与函数的单调性 专题一 含参函数单调性(单调区间) 微点1 含参函数单调性(单调区间)(一)——导主初等型(已下线)第四章 导数与函数的零点 专题四 导数中隐零点问题 微点4 导数中隐零点问题综合训练(已下线)模块三 大招13 恒成立参数——分类讨论广东省珠海市斗门区第一中学2023-2024学年高二下学期第一次月考数学试题(已下线)专题04 函数导数综合应用(四大题型)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(天津专用)