已知函數(shù)
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,其中
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為實數(shù).
(Ⅰ) 若
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在
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處取得的極值為
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,求
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的值;
(Ⅱ)若
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在區(qū)間
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上為減函數(shù),且
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,求
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的取值范圍.
試題分析:(1)由題意
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假設(shè)
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得
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此時
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所以
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無極值
(2)設(shè)
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,則有
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,
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設(shè)
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,
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,令
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解得
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或
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當(dāng)
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時
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為增函數(shù),當(dāng)
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時

為減函數(shù)
當(dāng)
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時,
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取得極大值
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,當(dāng)
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時,

取得極小值
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,且
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函數(shù)
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與
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有兩個公共點所以
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,或
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點評:中檔題,利用導(dǎo)數(shù)研究函數(shù)的極值,一般遵循“求導(dǎo)數(shù)、求駐點、研究導(dǎo)數(shù)的正負(fù)、確定極值”,利用“表解法”,清晰易懂。研究曲線有公共點的問題,往往利用導(dǎo)數(shù)研究函數(shù)圖象的大致形態(tài)加以解答。
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