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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