名校
解题方法
1 . 已知函数
,
,其中常数
.
(1)当
时,写出函数
的单调区间(无需证明);
(2)当
时,方程
有四个不相等的实根
.
①求
的乘积;
②是否存在实数
,使得函数
在区间
单调,且
的取值范围为
,若存在,求出
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/528c47af5e756030df86aef0798acc3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbeede118c407a800b05757b9a1393e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
②是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e333c856d24ba160c4623cbe335ca4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad8af7bed124f00c8e19b52d028b4d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2011高三上·山东菏泽·专题练习
2 . 已知函数
有如下性质:如果常数
,那么该函数在区间
上是减函数,在
上是增函数.
(1)如果函数
(
)的值域为
,求b的值;
(2)研究函数
(常数
)在定义域上的单调性,并说明理由;
(3)对函数
和
(常数
)作出推广,使它们都是你所推广的函数的特例.研究推广后的函数的单调性(只须写出结论,不必证明),并求函数
(n是正整数)在区间
上的最大值和最小值(可利用你的研究结论).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae543122a9a00feb76c84fd2ee6d1369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311f24add812e85cff437a699caa202e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c049415b40b1e5d3ddbd8c6b945c987c.png)
(1)如果函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33063230cfd1e497b93e1b87bc1a154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d875db0083b0b82f8864f1b25f7f7c7.png)
(2)研究函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c845cf8af8bfb0463e9797cc5628b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.png)
(3)对函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae543122a9a00feb76c84fd2ee6d1369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d74fef9c96eb3f55872919e7054f087a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/300f5517aa55c4c832e2008c18f436a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b448fe164c2c2931805e3b3847dcdd75.png)
您最近一年使用:0次
2021-09-25更新
|
1264次组卷
|
7卷引用:2021年陕西省渭南市韩城市高中数学竞赛试题
名校
3 . 已知函数
且
.
(1)判断函数
的奇偶性,并证明;
(2)若
,证明函数
在区间
上单调递减;
(3)是否存在实数
,使得
的定义域为
时,值域为
,若存在,求出实数
的取值范围;若不存在,则说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85e60be9b6817c1401cbd33d361dbd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466c3c575b0420a2d8a5843579059769.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320cba4d29e050a7e9f4e3b24bdbbc86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f5ce6cbcf094a780156547c4ce695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
4 . 已知函数
对任意实数x,
,满足条件
,
且当
时,
.
(1)求证:
是R上的递增函数;
(2)解不等式
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54dad48527a47eab4a5916ab0421cc71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb984de1cd94e043ebeb09dddae6c84a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78165f7cd39dc85a48ca9794290c626c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/736d35fb5b436cd822304eb8efdcefd3.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096651d50d2f45f4fa9b9e318253cade.png)
您最近一年使用:0次
2020-02-29更新
|
1124次组卷
|
5卷引用:陕西省西安市长安区第一中学2021-2022学年高一上学期期中数学试题