题目
题型:不详难度:来源:
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105335-54298.png)
(1)判断
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105335-43173.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105335-51786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105336-57110.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105336-10561.png)
(3)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105336-27098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105336-11086.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105336-75627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105337-29585.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105337-33524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105337-41192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105337-34458.png)
(3)在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105337-62217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105338-97935.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105338-32578.png)
解析
(1)利用定义法设出变量,然后代入函数解析式得到差值,然后变形定号,下结论得到。
(2)在第一问的基础上得到不等式的求解。
(3)要证明不等式恒成立,构造新函数利用函数的最小值大于等于零得到证明。
解:(1)由题得:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105338-55241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105338-22316.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105339-43330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105339-12983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105339-30975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105339-49386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105339-14714.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105340-68184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105340-84142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105337-33524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105337-41192.png)
(2)由(1)得:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105340-51648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105340-91561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105341-57614.png)
只要
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105341-26346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105337-34458.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105341-24910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105341-38177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105341-66539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105342-69208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105342-71350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105342-18326.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105342-26319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105342-71911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105343-35424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105343-27405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105342-71911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105343-47539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105343-55009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105343-50929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105344-78732.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105337-62217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105338-97935.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105338-32578.png)
核心考点
举一反三
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105311-82053.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105311-58209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105311-58529.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105312-96058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105312-60571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105312-10719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105312-40156.png)
(Ⅲ)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105313-96952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105313-52506.png)
设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105255-61043.png)
⑴当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105256-71678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105256-74487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105256-18097.png)
⑵若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105256-74487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105256-95177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105256-18097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105257-37540.png)
⑶在⑵的条件下,讨论函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105256-74487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105247-50610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105247-78283.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105248-77198.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105232-89610.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105232-43234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105232-91137.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105232-70052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105232-85182.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105232-27993.png)
(Ⅲ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105232-75362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105233-26718.png)
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105219-60781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105219-64752.png)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105219-68872.png)
(Ⅱ)若直线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105219-63419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105219-70478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105219-34376.png)
(Ⅲ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105220-98917.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105220-13876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105220-65737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018105220-84165.png)
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