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普通高中课程标准实验教科书数学选修1-1(人教A版)第93页练习4:求证:函数(fx)=2x3-6x2+7在(0,2)内是减函数。笔者在教学过程中发现可以由此题得到两个非常有用且在高考中也经常会遇到的结论,而且通过对这类问题的挖掘与引申激发了学生的学习兴趣和积极性,培养了学生的探究能力,获得了意外的惊喜。一、问题的解法思路1:因为(fx)=2x3-6x2+7,所以f(′x)=6x2-12x。当x∈(0,2)时,f(′x)=6x2-12x<0,因此函数(fx)=2x3-6x2+7在(0,2)内是减函数。
Ordinary High School Curriculum Standard Experimental Textbook Math Elective 1-1 (People Education, Version A) Page 93 Exercise 4: Proof: Function (fx) = 2x3-6x2 + 7 is a reduced function within (0,2). The author found in the teaching process can be obtained from this question two very useful and often encountered in college entrance examination conclusion, but also through the excavation and extension of such issues inspired students interest in learning and enthusiasm, training students Exploring ability, received unexpected surprises. First, the problem solution idea 1: Because (fx) = 2x3-6x2 +7, so f (’x) = 6x2-12x. When x∈ (0,2), f (’x) = 6x2-12x <0, so the function (fx) = 2x3-6x2 + 7 is a reduced function within (0,2).