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1 . 已知函数
和
有相同的最小值,(e为自然对数的底数,且
)
(1)求m;
(2)证明:存在直线
与函数
,
恰好共有三个不同的交点;
(3)若(2)中三个交点的横坐标分别为
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0166bbd15fa298c0d6a90a639108f4e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d6db457ee2d041b542c3eeff31d94cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
(1)求m;
(2)证明:存在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af79f45b5880c72a349500da9d8e118d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(3)若(2)中三个交点的横坐标分别为
![](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/b4c06ceee2b1e227de025476eee95672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5b965b3f27889e139013aa8c8f8fe3.png)
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2023-11-10更新
|
363次组卷
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4卷引用:福建省厦门第一中学2023-2024学年高一上学期期中考试数学试题
2 . 已知函数
,
.
(1)当
时求
的解集;
(2)当
时.若存在
使得对任意的
,都存在
使得
成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bc671967f99e86389595fb7d73fee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76c8dd9d8b65339df288b2d784e924f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f9d75ebbb4ebb290c4fd3444e1c38b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074482d083a7a0475d66ae29315ae311.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2bf33032e4f44ff4e9473e069dd8be5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b3a5b4f2b7279a7aa94f8ec12b3f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bb0589f9beda08f13663816e020df5.png)
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3 . 已知函数
.
(1)当
为何值时,
轴为曲线
的切线;
(2)用
表示
中的最小值,设函数
,讨论
零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6a039edbde7d4c242a5ef6cba5f853.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0898d7174604fa223558cb25b4c78b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061de6f5e53fd5724c5910b8f4ac8c9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
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4 . 已知函数
.
(1)求曲线
的单调区间;
(2)若函数
在
上有两个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc6a751a314af11b75aabca005f9439.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0384a0466920e5bf00231a5c5bf77969.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ca681ae72055316ef35c01fdb27034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
5 . 已知函数
.
(1)当a =1,b = -1时,求f (x)的极值;
(2)当
时,记函数
在区间
上的最大值为M,最小值为N,求M-N的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34274cdbfeada5f6d04130c0ecf0b222.png)
(1)当a =1,b = -1时,求f (x)的极值;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52145e80c9446eacbc6acc74f59cc4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
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6 . 设函数
,其中
.
(1)若当
时
取到最小值,求a的取值范围.
(2)设
的最大值为
,最小值为
,求
的函数解析式,并求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56cd2f6d01a2a61d67296dfee79917c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c895279c724791bfcafcd6e566c630db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760f804646698060703c5458ff5637c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84dd730984112f38e20298f165afa366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3369a9a5eeee1473518dc9f0e657e73e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
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名校
7 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b91b37696ffbad1a30a8bc5f4c6b252.png)
(1)求函数
的单调区间;
(2)对于任意
均有
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b91b37696ffbad1a30a8bc5f4c6b252.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97148e04ca6a9f9dca0aba91ce4e1d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab06a338f1af2a0f2f0b20964f4738ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-11-30更新
|
1506次组卷
|
6卷引用:【新东方】杭州新东方高中数学试卷397
(已下线)【新东方】杭州新东方高中数学试卷397(已下线)【新东方】杭州新东方数学试卷414浙江省杭州高级中学2020-2021学年高三上学期11月期中数学试题(已下线)黄金卷14-【赢在高考·黄金20卷】备战2021高考数学全真模拟卷(新高考专用)(已下线)文科数学-学科网2021年高三1月大联考考后强化卷(新课标Ⅲ卷)?河南省焦作市温县第一高级中学2021-2022学年高二上学期11月月考文科数学试题
19-20高一·浙江杭州·期末
名校
8 . 已知
,函数
.
(Ⅰ)证明:函数
在
上有唯一零点;
(Ⅱ)记
为函数
在
上的零点,证明:
.其中
…为自然对数的底数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/410e86d9c9c699f0f903769bd22e07db.png)
(Ⅰ)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79fe3414b32bbd1190b41ed8307f905.png)
(Ⅱ)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a7a4a037a4dfe973f1eb683d93d799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0369aee0b400b23f8cb8f0413431030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405dfcca25b76af059fb4c308983eae.png)
您最近一年使用:0次
2020-11-13更新
|
1081次组卷
|
7卷引用:【新东方】杭州新东方高中数学试卷356
(已下线)【新东方】杭州新东方高中数学试卷356浙江省杭州地区(含周边)重点中学2020-2021学年高三上学期期中数学试题江西省高安中学2020-2021学年高二上学期期末考试数学(理)试题(已下线)专题04函数与导数(测)-2021年高考数学二轮复习讲练测(新高考版)(已下线)专题04 函数与导数(测)-2021年高考数学二轮复习讲练测(文理通用)(已下线)专题17 导数的基本应用(测)(文科)第一篇 热点、难点突破篇-《2022年高考文科数学二轮复习讲练测》(全国课标版)(已下线)专题17 导数的基本应用(测)(理科)第一篇 热点、难点突破篇-《2022年高考理科数学二轮复习讲练测》(全国课标版)
名校
解题方法
9 . 已知
,函数
.
(1)若
,求函数
的值域;
(2)若函数
在
上不 单调,求实数
的取值范围;
(3)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/261c0899711077922ca479c99ffe2fef.png)
是函数
(
为实数)的其中两个零点,且
,求当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9fbbd9c88736e500f5251f97b08452.png)
变化时,
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3b9147459942e3344e3fc1e98298cd6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aadc68ed399afd6db385dae5e963c97a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/261c0899711077922ca479c99ffe2fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4baf7df076c898fa079b0f9349b3821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd16664b728b05f7e5597a390675420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9fbbd9c88736e500f5251f97b08452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
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10 . 已知函数
(
为负整数)的图象经过点
设
问是否存在实数
使得
在区间
上是减函数,且在区间
上是增函数?并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574d467c49349bfd1b8b0bf817b05b62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9dfdce64bc7d7250d2c7f60024bcf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cdc8239e137fcfe935a00fc7f3c159b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc3c5e9d853f4886bca8e187557f800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f27d9fb330f023ec36eeebb5c80049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/562a73679fa73cbac276b56d13343208.png)
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