题目内容
设函数
=x+ax2+blnx,曲线y=
过P(1,0),且在P点处的切斜线率为2.
(1)求a,b的值;
(2)证明:
≤2x-2.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011954023448.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011954023448.png)
(1)求a,b的值;
(2)证明:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011954023448.png)
(1)![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011954055549.png)
(2)![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119540701444.png)
而
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011954055549.png)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119540701444.png)
而
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119540861430.png)
试题分析:(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011954101886.png)
由已知条件得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119541331421.png)
解得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011954055549.png)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011954164978.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011954179761.png)
设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119541951185.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119542261182.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119542422359.png)
而
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119540861430.png)
点评:中档题,此类问题属于导数应用的基本问题,往往将单调性、极值、解析式等综合在一起进行考查,应掌握好基本解题方法和步骤。切线的斜率等于函数在切点的导函数值。在某区间,导函数值非负,则函数为增函数;导函数值非正,则函数为减函数。
![](http://thumb.zyjl.cn/images/loading.gif)
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