一道英语数学题an open rectangular box with a square base is to be made from 48ft^2 materiali.write a formula for the Volume and the Surface Area of the boxii.find the value of x for which V is maximum.
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一道英语数学题an open rectangular box with a square base is to be made from 48ft^2 materiali.write a formula for the Volume and the Surface Area of the boxii.find the value of x for which V is maximum.
一道英语数学题
an open rectangular box with a square base is to be made from 48ft^2 material
i.write a formula for the Volume and the Surface Area of the box
ii.find the value of x for which V is maximum.
一道英语数学题an open rectangular box with a square base is to be made from 48ft^2 materiali.write a formula for the Volume and the Surface Area of the boxii.find the value of x for which V is maximum.
设底面边长为a,高为h,则
a+2h=48
i：V=a^2*h=a^2*(48-a)/2ft^3
S=a^2+4*a*h=a^2+4*a*(48-4)/2=a^2+2*a*(48-a)ft^2
ii：假如x指的是底面边长,则
V=x^2*h=x^2*(48-x)/2求导
V'=48x-3x^2/2,当V'=0时,有
x=0ft(显然不合适,舍去),或x=32ft为所求
翻译：
用一张48平方英尺的材料制作一个没有封口的底面为正方形的长方体盒子。
1.写出盒子体积与表面积的公式
2.找到使体积V最大的x的值。
有疑问：x是什么?表面积？