题目
题型:解答题难度:一般来源:不详
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064903-61803.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064903-11673.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064904-39429.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064904-42996.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064904-89524.gif)
(I)当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064904-95970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064904-79485.gif)
(II)是否存在实数m,使
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064904-79485.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064905-77533.gif)
(III)求证:当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064905-74222.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064905-44247.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064905-60664.gif)
答案
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064905-80457.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064906-54459.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064906-97113.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064906-67489.gif)
(3) 略
解析
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064904-42996.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064904-95970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064905-80457.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064906-54459.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064906-97113.gif)
(II)方法一:假设存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064905-77533.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064904-79485.gif)
由(I)得到
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064906-34611.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064906-33786.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064906-38482.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064904-79485.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064907-98050.gif)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064907-44589.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064907-84422.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064907-39342.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064906-67489.gif)
经检验,此时
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064904-79485.gif)
所以存在
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064906-67489.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064904-79485.gif)
方法二:因为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064904-79485.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064907-50582.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064908-46451.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064908-46294.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064908-68105.gif)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064908-70022.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064908-88675.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064906-67489.gif)
经检验,此时
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064904-79485.gif)
所以存在
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064906-67489.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064904-79485.gif)
(III)因为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064909-27944.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064905-74222.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064909-33337.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064909-50631.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064909-79747.gif)
……
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064909-35011.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064910-80060.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064910-22744.gif)
因此只需取正整数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064910-24536.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064910-76031.gif)
核心考点
试题【 (本题满分14分)已知函数,其中.定义数列如下:,.(I)当时,求的值;(II)是否存在实数m,使构成公差不为0的等差数列?若存在,请求出实数的值,若不存在,】;主要考察你对一次函数的图象和性质等知识点的理解。[详细]
举一反三
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064853-44833.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064853-43376.gif)
⑴若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064853-97756.gif)
⑵当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064854-71003.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064854-70676.gif)
⑶当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064854-71502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064854-28759.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064854-38258.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064848-17600.gif)
(Ⅰ)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064849-64482.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064849-80542.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064849-75238.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064849-59303.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064849-64482.gif)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064849-64482.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064849-88206.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064850-83046.gif)
已知二次函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064843-46316.gif)
(1)求f(x)的解析式;
(2)若函
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064843-10017.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064843-10675.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064844-80006.gif)
已知
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064837-43862.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064837-98579.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819064837-70702.gif)
(1)当a=3时,求f(x)的零点;
(2)求函数y=f (x)在区间[1,2]上的最小值.
A.(4,+x) | B.(0,4) | C.(1,4) | D.(0,1) |
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