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在中学里研究函数极值問題,散見于二次函数与不等式各单元的习題中。課本内因缺乏明确的要求,学生在学习时往往不能深入地理解,因而感到困难。所以教师在不加深課本原有的深度下,通过复习,使学生能够較完整的掌握这部分知識,还是必要的。現就这方面試作較为綜合系統的說明,以供参考。一、求二次函数的极值問題。在高一代数“二次函数”这一单元里,学生就初次遇到求二次函数的极大值与极小值問題,此时教师在讲了二次函数y=ax~2++bx+c的图象后,可以指出,从y=ax~2+bx+c图象里,我們很清楚地看到:在(1)a>0的时候,函数图象的拋物綫口向上,它的纵坐标由递減轉为递增,这个頂点的纵坐标相当于极小值。(2)a<0的时候,拋
In the middle school, the problem of function extremum is studied in the exercises of each unit of quadratic function and inequality. Due to the lack of clear requirements in the textbooks, students often do not have a good understanding of it when they are studying, and therefore feel difficult. Therefore, teachers do not need to deepen the original depth of the textbooks, so that students can grasp this part of the knowledge in a more complete way, which is still necessary. The description of the more comprehensive system in this area is now for reference. First, find the quadratic function of the extreme problem. In the unit of “quadratic function” of the higher generation number, the student first encountered the problem of finding the maximum and minimum values of the quadratic function. At this time, the teacher is talking about the quadratic function y=ax~2++bx. After the image of +c, it can be pointed out that from the y=ax~2+bx+c image, we can clearly see that when (1)a>0, the parabola of the function image is upward. Its ordinate changes from decreasing to increasing. The ordinate of this vertex corresponds to the minimum value. (2) When a<0, throw