(本小題滿分15分)已知函數(shù)
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且
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.
(Ⅰ)試用含
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式子表示
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;(Ⅱ)求
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的單調(diào)區(qū)間;(Ⅲ)若

,試求
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在區(qū)間

上的最大值.
(Ⅰ)
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(Ⅱ)
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在
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上單調(diào)遞增,在
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上單調(diào)遞減(Ⅲ)
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:(Ⅰ)
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的定義域為
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…2分
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,
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得:
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……4分
(Ⅱ)將
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代入:
得
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……6分
當(dāng)
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時,
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由
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,得
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又
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即
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在

上單調(diào)遞增
當(dāng)
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時,
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由
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,得
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又

即
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在

上單調(diào)遞減
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在
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上單調(diào)遞增,在

上單調(diào)遞減…………9分
(Ⅲ)當(dāng)
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,即
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時,
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在
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上單調(diào)遞增
所以

…11分
當(dāng)
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,即
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時,
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在

上單調(diào)遞增,在

上單調(diào)遞減
所以

………13分
當(dāng)

時,
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在
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上單調(diào)遞減
所以
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……15分
綜上:
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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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

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
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
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a,

,

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
在

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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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(2)當(dāng)

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
,均有

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
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(3)若

,對任意

、

,且

,試比較

與

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
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
,設(shè)函數(shù)

,其中

為非零常數(shù)
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
的解析式;
(II)當(dāng)

時,判斷函數(shù)

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(III)證明:對任意的正整數(shù)

,不等式

恒成立
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題型:解答題
已知函數(shù)
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,
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,設(shè)
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.
(Ⅰ)求函數(shù)
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的單調(diào)區(qū)間;
(Ⅱ)若以函數(shù)
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圖像上任意一點
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為切點的切線的斜率
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恒成立,求實數(shù)
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的最小值;
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