题目
题型:解答题难度:简单来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052842-24560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052842-98424.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052843-12519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052843-45748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052843-13473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052843-62180.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052843-97334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052844-21431.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052844-97558.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052844-51986.png)
(2)当a≥3时,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052844-38175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052844-56040.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052844-53884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052844-38175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052844-56040.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052845-95385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052845-26898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052845-96408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052845-77274.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052845-17386.png)
(2) 构造函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052846-29200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052846-40710.png)
分别研究
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052846-44232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052846-55427.png)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052846-88769.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052845-26898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052847-21377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052847-23944.png)
由条件,得
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052847-52590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052847-52969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052844-51986.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052845-77274.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052847-54323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052848-42682.png)
由条件,得
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052848-21290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052848-76613.png)
综合①,②得b的取值范围是
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052844-51986.png)
(2)令
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052846-29200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052846-40710.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052846-44232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052848-57242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052848-19714.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052846-44232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052848-79132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052849-92991.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052849-23188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052849-41313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052849-90325.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052846-55427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052849-34619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052850-38871.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052849-41313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052849-90325.png)
又因为函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052849-41313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052850-42311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052849-41313.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052850-62795.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052850-84911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052850-86196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052851-58180.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052844-38175.png)
当a≥3时,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052844-38175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052844-56040.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052844-53884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052844-38175.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052844-56040.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052836-89132.png)
(I)证明:函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052836-80093.png)
(II)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052836-87302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052834-33619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052832-88616.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052832-30664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052832-98712.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052833-24499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052832-98712.png)
③函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052832-98712.png)
④方程
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052833-83061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052828-50332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052828-75890.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052828-24754.png)
(2)判断函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052829-93927.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052829-83452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052829-48985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052824-63079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052824-84614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052824-68639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052825-51693.png)
(1)求满足不等式
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052825-63115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052825-20263.png)
(2)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052825-36019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052825-80507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052826-74122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052826-25566.png)
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