【题文】( )A.>0B.>-3C.<1D.
题型:难度:来源:
【题文】
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064846-85003.png)
( )
答案
【答案】D
解析
【解析】
试题分析:方法一:由
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064847-67024.png)
,可得
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064847-62548.png)
,化简得
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064847-77969.png)
,要使对于任意正整数n都成立,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064848-40077.png)
,即
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064848-87031.png)
.
方法二:因
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064849-35622.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064849-20798.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064849-24380.png)
上为单调递增函数,但考虑到
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064850-50254.png)
为二次函数,且单调性只需满足整数点,所以二次函数的对称轴
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064850-32055.png)
(满足
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064850-29843.png)
,而不是对称轴
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064851-45848.png)
),解得
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064847-81588.png)
.
考点:函数的恒成立问题(一般采用分离常数法).
举一反三
【题文】已知函数f(x)=
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064839-61893.png)
,对任意的x∈[0,1]恒有f(x
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064826-83604.png)
.
(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064826-12432.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064826-39942.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064826-93503.png)
的单调区间;
(2)若对任意
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064826-83479.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064826-62760.png)
,试比较
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064826-15363.png)
与
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064827-14649.png)
的大小.
【题文】已知函数f(x)=
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064823-12518.png)
,对任意的x∈[0,1]恒有f(x
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064806-74984.png)
.
(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064806-83412.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064807-23682.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064807-81652.png)
的单调区间;
(2)若对任意
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064807-18133.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064807-52046.png)
,试比较
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064808-25335.png)
与
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064808-70613.png)
的大小.
【题文】已知二次函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064732-38018.png)
:
(1)若函数的最小值是-60,求实数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064732-38786.png)
的值;
(2)若函数在区间
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064732-37490.png)
上存在零点,求实数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327064732-38786.png)
的取值范围.
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