题目内容
设函数
.
(1)当
时,求函数
的单调区间;
(2)当
时,若
恒成立,求
的取值范围.
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(1)当
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(2)当
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(1)函数
单调增区间为
,单调减区间为
;(2)
.
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试题分析:(1)此类题目考查利用导数研究函数的单调性,解法是:求函数的导数,令导数大于零,解得单调增区间(注意函数的定义域),令导数小于零,解得单调减区间(注意定义域);(2)先将不等式
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试题解析:(1)函数
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当
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当
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当
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所以,函数
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(2)因为
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所以
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即
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法一:令
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所以
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因为
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所以
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又因为
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所以
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要使
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所以
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法二:因为
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令
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因为
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因此
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所以
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所以
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