题目内容
已知函数
,
(其中
,
),且函数
的图象在点
处的切线与函数
的图象在点
处的切线重合.
(Ⅰ)求实数a,b的值;
(Ⅱ)若
,满足
,求实数
的取值范围;
(Ⅲ)若
,试探究
与
的大小,并说明你的理由.
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(Ⅰ)求实数a,b的值;
(Ⅱ)若
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(Ⅲ)若
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(Ⅰ)
,
;(Ⅱ)
;(Ⅲ)
.
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试题分析:(Ⅰ)先求出
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(Ⅲ)令
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试题解析:(Ⅰ)∵
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又
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由
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(Ⅱ)由
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令
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①当
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②当
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∵
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故
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所以
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综合①②得实数m的取值范围是
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(Ⅲ)令
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令
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∴当
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故函数
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故对于任意
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又∵
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∴
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∴
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