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

,则

∴ 函数是单调增函数

∴ 命题成立··························································································· 12分

【解析】略

 

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