1 . 为宣传平潭综合试验区的“国际旅游岛”建设,试验区某旅游部门开发了一种旅游纪念产品,每件产品的成本是12元,销售价是16元,月平均销售
件.后该旅游部门通过改进工艺,在保证产品成本不变的基础上,产品的质量和技术含金量提高,于是准备将产品的售价提高.经市场分析,如果产品的销售价提高的百分率为
,那么月平均销售量减少的百分率为
.记改进工艺后,旅游部门销售该纪念品的月平均利润是
(元).
(1)写出
与
的函数关系式;
(2)改进工艺后,确定该纪念品的售价,使该旅游部门销售该纪念品的月平均利润最大.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e4dfb68af91a58e45ca8596abc3d96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0a89e3c30f6e4d4c5db4378b05d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)改进工艺后,确定该纪念品的售价,使该旅游部门销售该纪念品的月平均利润最大.
您最近一年使用:0次
名校
解题方法
2 . 设函数
,其中
和
是实数,曲线
恒与
轴相切于坐标原点.
(1)求常数
的值;
(2)当
时,关于
的不等式
恒成立,求实数
的取值范围;
(3)求证:对于任意的正整数
,不等式
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d898c0ea26601b90dccfb8c11ae4712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e46371f310e03a153a1698aad9d4c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:对于任意的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed08261f7e9b82eb1906cca1abff1a6.png)
![](https://img.xkw.com/dksih/QBM/2017/8/15/1752670428037120/1753289400385536/STEM/36cda1a30cef44fd841f3865b20ba631.png?resizew=3)
您最近一年使用:0次
3 . 已知函数
,其中
.
(1)若
,求证:当
时,
成立;
(2)若
,判断函数
的零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73943a7566c5fdd60e7122c3cdbd869d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0372e386405ede82b72a0f268b741c50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4220892627ceb9562b815430a2f8b99a.png)
您最近一年使用:0次
2017-07-12更新
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278次组卷
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2卷引用:福建省泉州市泉港区一中2016-2017学年高二下学期期末考试数学(理)试题