2010·浙江·一模
解题方法
1 . 已知函数![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/5e64765754e44a58816d5b46210b9a89.png?resizew=12)
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/bb267d8852d6434d908feeeec0175a8f.png?resizew=234)
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/5e64765754e44a58816d5b46210b9a89.png?resizew=12)
.
(Ⅰ)求函数
的单调区间;
(Ⅱ)若函数
的图像在点
处的切线的斜率为
,问:
在什么范围取值时,对于任意的
,函数
在区间
上总存在极值?
(Ⅲ)当
时,设函数
,若在区间
上至少存在一个
,使得
成立,试求实数
的取值范围.
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/5e64765754e44a58816d5b46210b9a89.png?resizew=12)
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/bb267d8852d6434d908feeeec0175a8f.png?resizew=234)
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/5e64765754e44a58816d5b46210b9a89.png?resizew=12)
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/5e64765754e44a58816d5b46210b9a89.png?resizew=12)
(Ⅰ)求函数
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/eabb122f339b4673a115fe5493b27314.png?resizew=36)
(Ⅱ)若函数
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/9961606044494457a31de3585628468b.png?resizew=61)
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/d3893716caf54b31b91c6acfd4d61ba2.png?resizew=60)
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/20d90ee520a44200b95624553199767f.png?resizew=9)
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/37649954997f4e31818df3de7b59f01a.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/9409476e3b564e78a828efda9522c030.png?resizew=52)
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/96a5d13fb62749ba9ae7c80cef0bb276.png?resizew=172)
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/18cc7564ddac4050b8a9f2badb6d14d2.png?resizew=32)
(Ⅲ)当
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/f1fb9026bfef46ca8ad18667df9ff3dc.png?resizew=39)
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/35e2ec5761734780b95ccd82108c3ac9.png?resizew=184)
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/02f0912425bf4d37a37ab981974e9134.png?resizew=32)
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/3f65fc70aa3649b0b80daee804cd5bea.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/671a0b8b01324a4082b28231e1c55ee2.png?resizew=95)
![](https://img.xkw.com/dksih/QBM/2011/12/31/1570670850367488/1570670856126464/STEM/6ae026eb70fb47c6b9379a339c371c56.png?resizew=16)
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2 . 已知函数
的图象与x轴有3个公共点,则c的取值范围是______ ;若函数
在区间
上的最大值为2,则m的最大取值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e3170e07678277d375a6aad4a172f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/359baaa1ce86fe2403796f44d62429fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4993051ff019debe00c1a01edf44d0b9.png)
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2021-07-15更新
|
232次组卷
|
2卷引用:浙江省杭州市学军中学2020-2021学年高二下学期期中数学试题
名校
解题方法
3 . 已知函数
,其中
,
为自然对数的底数.
(1)当
时,对
,
①证明:
;
②若
恒成立,求实数
的范围;
(2)若函数
在
上存在极值,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1604d09f3a06f97537ea339a87bffc28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7364911f4597bfe996da15bf929c7fe.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81ed7f6a4475e0fa682fa81ee747da3.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347b78cd077f35923490915f5220c332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f00f2f6ab162f9333ec55db195d663b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 已知
,从原点
作
图像的切线,切点为
,已知
,其中
为自然对数的底数.
(1)求
的值;
(2)若
有两个极值点
,
,
(i)求参数
的范围;
(ii)若假定
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3434b4830060fbd6885e05ccee93118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/413a244b5a621d2f80d3c99733501c33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f59088c3ad094cb5d9c1252dc2c63a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(i)求参数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(ii)若假定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b5e06a1a78a6215b890741e5624a6c9.png)
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5 . 已知函数
.
(1)若
求方程
的解集;
(2)若
有两个零点且有两个极值点,记两个极值点为
,
①求
的取值范围;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad084d3bce1e2de2bf59a9a981fc9912.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8603ae7a8417d09605fa706e31d3dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9694eaaa274ed8e3774a100aff5f101.png)
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6 . 若不等式
在区间
内的解集中有且仅有三个整数,则实数
的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b172fa37f1825a4b4c0f1111bdf50bde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2020-04-06更新
|
3477次组卷
|
10卷引用:2020届百校联盟TOP300八月尖子生联考(全国II卷)文科数学试题
2020届百校联盟TOP300八月尖子生联考(全国II卷)文科数学试题2020届百校联盟TOP300八月尖子生联考理科数学(全国II卷)试题2020届百校联考高考考前冲刺必刷卷(二)数学(理)试题2020届百校联考高考考前冲刺必刷卷(二)数学(文)试题(已下线)第27练 不等式的综合应用-2021年高考数学(文)一轮复习小题必刷江苏省无锡市天一中学2021届高三下学期二模考前热身模拟数学试题湖北省襄阳市第四中学2021届高三下学期一模数学试题(已下线)第9讲 函数中的整数问题与零点相同问题-2022年新高考数学二轮专题突破精练(已下线)专题3-2 压轴小题导数技巧:求参 - 2河南省郑州外国语学校2021-2022学年高三上学期调研考试三理科数学试题
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7 . 已知二次函数
,关于
的不等式
的解集为
,其中
.
(1)求
的值;
(2)令
,若函数
存在极值点,求实数
的取值范围,并求出极值点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0958781bd1c23a3afbe2f77b08a571c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc16399997386b7ec065f04731bcce81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edf9a3042215eceebc8c48a2648c47e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03b011f69dfc5262a3d82f64676739b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e357538192b0086515ca082025dad9b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24ae93af9569df6f519c4fe2dad87228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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