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例1(2013年浙江省高考理数最后一题)已知a∈R,函数f(x)=x3-3x2+3ax-3a+3,当x∈[0,2]时,求f(x)的最大值.从正面做,是三次函数图像的翻折问题,对学生的分类讨论能力和运算能力的要求都有很高,大多数学生是望而生畏.换一个角度来做,把函数看成关于a的一次函数g(a)=3 x(-1)a+x3-3x2+3,此时x为参数.问题变成直线的翻折问题,当x∈[0,2]时,y=g(a)是一系列的直线族,可以代表性地画出3条:当
Example 1 (last year’s college entrance examination in Zhejiang Province in 2013) Known a∈R, function f(x)=x3-3x2+3ax-3a+3, when x∈[0,2], find f(x) The maximum value. From the front, it is the problem of the rewinding of the three-function image. The requirements for the students’ classification and discussion skills and the computing ability are very high. Most students are daunting. To do it from another perspective, the function is regarded as The primary function of a is g(a)=3 x(-1)a+x3-3x2+3. At this time, x is a parameter. The problem becomes a straight-line folding problem. When x∈[0,2], y= g(a) is a series of linear families that can be drawn representatively 3: When