(1)设高h,V=(6-2h)^2×h
=(36-24h十4h^2)×h
=36h-24h^2十4h^3
求极值,
求导=36-48h十12h^2
=12(h^2-4h十3)
=12(h-1)(h-3)
h1=1,V1=(6-1×2)^2×1=16
h2=3,V2=(6-2×3)^2×1
=0
h=2
时有极大值。
V最大=(6-2)^2×2
=
追答(2)设正方形底边长x,高h=32000/x^2
纸板总面积y=x^2十4xh
=x^2十128000/x
y'=2x-128000/x^2
=2(x^3-64000)/x^2
=0
x=³√64000
=10׳√64
=40cm
h=32000/x^2
=32000/1600=20