Posted by Derek on Monday, October 29, 2012 at 8:51pm.
base --- x by x ft
height -- y ft
area = 4xy + x^2
192 = 4xy + x^2
y = (192 - x^2)/(4x)
V = x^2 y
= x^2 (192-x^2)/(4x)
= 48x - (1/4)x^3
dV/dx = 48 - (3/4)x^2 = 0 for a max of V
(3/4)x^2 = 48
x^2 = 64
x = 8
then y = (192-64)/(32) = 4
max Volume = (8^2)(4) = 256
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