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有些数学题,初看起来难以下手,令人生畏,但是,引入一个新参数——“平均量”后,却有“山重水复疑无路,柳暗花明又一村”的轻快之感,顺利解决问题。本文将简要介绍平均量代换在解题中的几种应用。一在求函数最值中的应用 [例1] 求函数y=f(x)=x(x+1)(x+2)(x+3)的最小值。解:函数是含自变量x的四个因式的乘积,取这四个量的平均量作代换。
Some mathematics questions may seem daunting at first glance. However, after introducing a new parameter, the “average amount”, there is a sense of briskness in the “reinvention of the mountain and the reunification of the mountains and the flowers”. problem. This article will briefly introduce several applications of average quantity substitution in problem solving. The application of a function in the most value [Example 1] Find the minimum value of the function y=f(x)=x(x+1)(x+2)(x+3). Solution: The function is a product of four factors with the independent variable x, and the average of these four quantities is substituted.