题目内容
已知函数
,
(1) 若f(x)在区间[m,m+1]上单调递减,求实数m的取值范围;
(2) 若f(x)在区间[a,b](a<b)上的最小值为a,最大值为b,求a、b的值。
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823193741751738.png)
(1) 若f(x)在区间[m,m+1]上单调递减,求实数m的取值范围;
(2) 若f(x)在区间[a,b](a<b)上的最小值为a,最大值为b,求a、b的值。
(1)
的对称轴为
.
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231937417981037.png)
故
在
上单调递增.
为方程
的两根
由![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823193741907968.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823193741767463.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823193741782781.png)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231937417981037.png)
故
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823193741767463.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823193741845437.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823193741860889.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823193741876511.png)
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823193741907968.png)
略
![](http://thumb2018.1010pic.com/images/loading.gif)
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