已知函数
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102747346860844/SYS201311031027473468608020_ST/0.png)
.(a为常数,a>0)
(Ⅰ)若
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102747346860844/SYS201311031027473468608020_ST/1.png)
是函数f(x)的一个极值点,求a的值;
(Ⅱ)求证:当0<a≤2时,f(x)在
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102747346860844/SYS201311031027473468608020_ST/2.png)
上是增函数;
(Ⅲ)若对任意的a∈(1,2),总存在
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131103102747346860844/SYS201311031027473468608020_ST/3.png)
,使不等式f(x
)>m(1-a
2)成立,求实数m的取值范围.
考点分析:
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