一道英语数学题an open rectangular box with a square base is to be m
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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 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.
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 m](/uploads/image/z/3288885-69-5.jpg?t=%E4%B8%80%E9%81%93%E8%8B%B1%E8%AF%AD%E6%95%B0%E5%AD%A6%E9%A2%98an+open+rectangular+box+with+a+square+base+is+to+be+m)
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
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
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