已知函數(shù)

在
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處取得極值.
(Ⅰ)求函數(shù)

的單調(diào)區(qū)間;
(Ⅱ)求證:
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,


.
(1)函數(shù)
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的單調(diào)增區(qū)間為
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,
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,單調(diào)減區(qū)間為
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.
(2)見解析
(Ⅰ)
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由
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得
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…………………………4分
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,

故函數(shù)

的單調(diào)增區(qū)間為
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,
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,單調(diào)減區(qū)間為

.
……………………………………8分
(Ⅱ)由(Ⅰ)

在
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遞增,在
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遞減,

遞增,在

時取極大值
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又


.



∴在

上,


.
又
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故

(當(dāng)且僅當(dāng)

時取等號).
即

的最小值為
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.


,
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.……………………12分
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科目:高中數(shù)學(xué)
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
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在
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
對于一切
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
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來源:不詳
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已知

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
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
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
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
是直線

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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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
在區(qū)間

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
上的最小值.

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
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
上變化時,證明:
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
是偶函數(shù),當(dāng)

時.

(a為實(shí)數(shù)).

(1)若

在

處有極值,求a的值。(6分)
(2)若

在

上是減函數(shù),求a的取值范圍。(8分)
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