在人教版高中数学第二册(上)的P.30,学习均值不等式时,有这样一道习题: (1)在面积为定值的扇形中,半径是多少时扇形周长最小? (2)在周长为定值的扇 形中,半径是多少时扇形面积最大? 解(1)S刷=1/2lr=定值,则l=2S/r 所以 当2S/r=2r时,上式取“=”号,即r=S~(1/S)时,扇形的周长最小, (2)C刷=l+2r=定值,则l=C-2r. 所以 当C-2r=2r时,上式取“=”号,即r=C/4时,扇形的面积最大. 点评抓住给定的定值,将要研究最值的几何量表示为半径r的函数式,分别 In P.30 of the Second Edition of the Mathematics Education High School Mathematics Book (top), when studying the mean inequality, there is such an exercise: (1) What is the radius of the fan-shaped perimeter when the area is a fixed fan? What is the radius of the sector when the circumference is a constant fan? Solution (1) S brush = 1/2lr = fixed value, then l = 2S/r So when 2S/r = 2r, Take “=”, that is, when r=S~(1/S), the circumference of the sector is the minimum, (2)C brush=l+2r=value, then l=C-2r. So when C- When 2r=2r, the above equation takes the “”=" sign, that is, when r=C/4, the area of ​​the sector is the largest. Commenting on the given value, the geometric quantity to be studied is expressed as a function of radius r. Type, respectively