题目
题型:填空题难度:简单来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052638-44185.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052639-98920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052639-92330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052639-18410.png)
至少存在一点,使得以该点为圆心,1为半径的圆与圆
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052639-98920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052639-80050.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052639-81015.png)
【考点】圆与圆的位置关系,点到直线的距离
解析
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052639-90276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052640-20208.png)
∵由题意,直线
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052639-18410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052640-19075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052639-98920.png)
∴存在
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052640-93316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052640-80382.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052640-64289.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052641-43006.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052639-98920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052639-18410.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052641-94383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052641-38499.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052641-84324.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052639-80050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052639-81015.png)
核心考点
举一反三
设函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052631-70044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052632-68876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052632-73488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052632-33241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052632-10669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052625-71363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052626-15848.png)
已知x=1是函数f(x)=mx3-3(m+1)x2+nx+1的一个极值点,其中m,n∈R.
(1)求m与n的关系式;
(2)求f(x)的单调区间;
(3)当x∈[-1,1]时,m<0,函数y=f(x)的图象上任意一点的切线斜率恒大于3m,求m的取值范围.
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052612-94306.png)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052612-62548.png)
(Ⅱ)令函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052612-32976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052612-97584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052613-67333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052613-24522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052604-14713.png)
(Ⅰ)若曲线
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052604-98821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052604-91527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052604-61332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052604-98821.png)
(Ⅱ)若对于
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052604-94385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052605-49741.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052605-14934.png)
(Ⅲ)记
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052605-71291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052605-31128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052605-33084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052606-75957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818052606-81816.png)
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