(本小題滿分14分)
已知函數(shù)

,
(I)當

時,求函數(shù)

的極值;
(II)若函數(shù)

在區(qū)間
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上是單調(diào)增函數(shù),求實數(shù)
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的取值范圍.
(I)因為
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, …………… 2分
所以當
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時,
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,

…………… 3分
令
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,則

, …………… 4分
所以

的變化情況如下表:
……………5分
所以

時,

取得極小值

. ……………6分
(II) 因為

,函數(shù)
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在區(qū)間

上是單調(diào)增函數(shù),
所以
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對


恒成立.

……………8分
又

,所以只要

對


恒成立, ……………10分
解法一:設
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,則要使
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對


恒成立,
只要

成立, ……………12分
即

,解得

. ……………14分
解法二:要使
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對
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
恒成立,
因為

,所以

對
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
恒成立, ……………10分
因為函數(shù)

在

上單調(diào)遞減, ……………12分
所以只要

.

……………14分
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

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
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
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
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
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
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
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
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
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
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
[4,6]時,

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
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時,

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