问题　己知 f(x) =x2 +bx +c ,求证 :| f(1) | ,| f(2 ) | ,| f(3) |中至少有一个不小于 12 .分析 :通过观察可明显看出此题可用反证法 ,但证明一道题可能有几种方法 ,从正面入手也未必不可 ,现就上述两法进行具体讨论 .证明　反证法 1:假设 | f(1) | ,|f(2 ) | ,| f(3) |都小 The problem is known as f(x) = x2 + bx +c, verify: | f(1) |, | f(2) |, | f(3) | At least one of them is not less than 12. Analysis: Observable by observation It can be seen that this question can be used to prove the subject. However, there may be several ways to prove a question. It may not be possible to start from the front. Now we will discuss the above two methods in detail. Prove the anti-evidence method 1: Assume |f(1) |, |f(2) |, | f(3) | all small