設(shè)函數(shù)
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,
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.
(Ⅰ)當(dāng)
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時(shí),
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取得極值,求

的值;
(Ⅱ)若
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在
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內(nèi)為增函數(shù),求

的取值范圍.
(Ⅰ)
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(Ⅱ)
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本試題主要是考查導(dǎo)數(shù)的幾何意義的運(yùn)用以及導(dǎo)數(shù)求解函數(shù)的單調(diào)區(qū)間的極值的綜合運(yùn)用。
(1)由題意:
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解得
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.
(2)方程

的判別式
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,根據(jù)判別式符號(hào)來證明得到。
解:
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,
(Ⅰ)由題意:
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解得
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. ………………3分
(Ⅱ)方程
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的判別式

,
(1) 當(dāng)
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, 即
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時(shí),
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,
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在
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內(nèi)恒成立, 此時(shí)
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為增函數(shù); ------ 6分
(2) 當(dāng)
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, 即
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或
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時(shí),
要使
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在
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內(nèi)為增函數(shù), 只需在
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內(nèi)有
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即可, 設(shè)
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,
由
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得
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, 所以
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.
由(1) (2)可知,若
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在
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內(nèi)為增函數(shù),

的取值范圍是
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.---12分
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