题目内容
(本小题满分12分)已知二次函数
对任意实数x都满足
,且
.令
.
(1)求
的表达式;
(2)设
,证明:对任意
,恒有
.
【答案】
解:(1) 设
∴![]()
∴
又 ∵
,则![]()
∴
················································································ 5分
(2) ∵ 对![]()
∴
在[1,m]内单调递减
于是![]()
······························· 8分
记
,则
![]()
∴ 函数
在
是单调增函数
∴ ![]()
∴ 命题成立··························································································· 12分
【解析】略
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