题目内容
已知函数
,其中a>0.
(Ⅰ)求函数
的单调区间;
(Ⅱ)若直线
是曲线
的切线,求实数a的值;
(Ⅲ)设
,求
在区间
上的最大值(其中e为自然对的底数)。
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(Ⅰ)求函数
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(Ⅱ)若直线
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(Ⅲ)设
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(Ⅰ)函数
的单调递增区间为(0,2),递减区间为(-∞,0)和(2,+∞);(Ⅱ)
;(Ⅲ)
在区间
上的最大值为0.
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试题分析:(Ⅰ)求函数
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试题解析:(Ⅰ)①
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令
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∴函数f(x)的单调递增区间为(0,2),递减区间为(-∞,0)和(2,+∞)(4分)
(II)设切点为
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(III)
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令
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①当
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②当
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若
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若
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③当
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综上所述,
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