(本小題滿分12分)
設(shè)
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,當(dāng)
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時,對應(yīng)
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值的集合為
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.
(1)求
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的值;(2)若

,求該函數(shù)的最值.
(1)

.(2)當(dāng)

時,該函數(shù)取得最大值

本試題主要是考查了二次函數(shù)的最值和二次函數(shù)的解析式的求解。
(1)因為
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即
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,則

為其兩根,
由韋達(dá)定理知:
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所以
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,同理

,可知m,n的值。
(2)因為由(1)知:
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,那個根據(jù)對稱軸和定義域的關(guān)系而可知函數(shù)的最值。
解:(1)
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即
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,則

為其兩根,
由韋達(dá)定理知:

所以
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,

所以

.
(2)由(1)知:

,
因為
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,所以,當(dāng)

時,該函數(shù)取得最小值

,
又因為
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
,
所以當(dāng)

時,該函數(shù)取得最大值

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