试题分析:(I)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055939465.png)
=3
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055955338.png)
-2
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055970266.png)
-1若
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055939465.png)
=0,则
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055970266.png)
==-
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010056064327.png)
,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055970266.png)
=1
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055970266.png)
变化时,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055939465.png)
,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055845447.png)
变化情况如下表:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055970266.png)
| (-∞,- )
| -![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010056064327.png)
| (- ,1)
| 1
| (1,+∞)
|
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055939465.png)
| +
| 0
| -
| 0
| +
|
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055845447.png)
| ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010056235194.png)
| 极大值
| ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010056235194.png)
| 极小值
| ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010056235194.png)
|
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055845447.png)
的极大值是
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055877806.png)
,极小值是
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055892533.png)
--------8分
(II)由(I)可知,取足够大的正数时,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055845447.png)
>0,取足够小的负数时有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055845447.png)
<0,
结合
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055845447.png)
的单调性可知:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010056391543.png)
<0,或
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010056407283.png)
-1>0时,曲线
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010056423310.png)
=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055845447.png)
与
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055970266.png)
轴仅有一个交点,
∴当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055923807.png)
∪(1,+∞)时,曲线
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010056423310.png)
=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055845447.png)
与
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824010055970266.png)
轴仅有一个交点。 14分
点评:做此题的关键是分析出:要满足题意只需极大值小于0或者极小值大于0.考查了学生分析问题,解决问题的能力。属于中档题型。