關於微分的文字應用題.

直立圓柱形罐的表面面積= 600Pi
2(Pi)rh + 2(Pi)r^2 = 600Pi
rh + r^2 = 300
h = (300 - r^2) / r

直立圓柱形罐的體積,
V = (Pi) r^2 h = (Pi) r^2 (300 - r^2) / r = 300(Pi)r - (Pi)r^3
dV/dr = 300(Pi) - 3(Pi)r^2
Set dV/dr = 0,
300(Pi) - 3(Pi)r^2 = 0
r^2 = 100
r = 10 or -10 (rejected)
dV^2/d2r = 0 - 6(Pi)r
As r>0, dV^2/d2r <0 (Max)

所以，當底半徑為10cm 時其體積就是最大。