解:(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300505816.gif)
,由已知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300521315.gif)
,
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300552407.gif)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300568447.gif)
,解得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300693380.gif)
或
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300895231.gif)
.……………………………2分
又因?yàn)?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300911241.gif" style="vertical-align:middle;" />,所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300693380.gif)
.………………………………………………………………4分
(2)函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300131270.gif)
的定義域?yàn)?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300973410.gif" style="vertical-align:middle;" />,…………………………………………………5分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231923010981935.gif)
,
①當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301114294.gif)
,即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301129231.gif)
時,
由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301145332.gif)
得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301301358.gif)
或
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301301316.gif)
,
因此函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300131270.gif)
的單調(diào)增區(qū)間是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301332328.gif)
和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301348444.gif)
.…………………………………6分
②當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301363294.gif)
,即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301457280.gif)
時,
由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301145332.gif)
得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301504267.gif)
或
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301519404.gif)
,
因此函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300131270.gif)
的單調(diào)增區(qū)間是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301551414.gif)
和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301566444.gif)
.…………………………………7分
③當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301582281.gif)
,即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301597226.gif)
時
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301613342.gif)
恒成立(只在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301629348.gif)
處等于0),
所以函數(shù)在定義域
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300973410.gif)
上是增函數(shù). …………………………………………………8分
綜上:①當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301129231.gif)
時,函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300131270.gif)
的單調(diào)增區(qū)間是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301332328.gif)
和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301348444.gif)
;
②當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301457280.gif)
時,函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300131270.gif)
的單調(diào)增區(qū)間是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301551414.gif)
和
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301566444.gif)
;
③當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192301597226.gif)
時,函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300131270.gif)
的單調(diào)增區(qū)間是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300973410.gif)
.………………………………9分
(3)當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300693380.gif)
時,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192302580781.gif)
,由(2)知該函數(shù)在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192302580335.gif)
上單調(diào)遞增,因此在區(qū)間
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192302596269.gif)
上
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300131270.gif)
的最小值只能在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300303220.gif)
處取到. ……………………………10分
又
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192302892487.gif)
,………………………………………………………………11分
若要保證對任意
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300365329.gif)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192303033463.gif)
恒成立,應(yīng)該有
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192303064346.gif)
,即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192303079386.gif)
,解得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192303111294.gif)
,…………………………………………………13分
因此實(shí)數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192300490192.gif)
的取值組成的集合是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823192303189399.gif)
.………………………14分