Posted by Anonymous on Friday, April 20, 2012 at 1:31pm.
cut squares of length x
v = x(8.5-2x)^2 = 72.25x - 34x^2 + 4x^3
dv/dx = 72.25 -68x + 12x^2
max/min achieved at x = 17/12 or 17/4
Just knowing about the shape of cubics, it's clear that 17/12 is where the max volume occurs.
So, the box is 8.5-17/6 x 8.5-17/6 x 17/12 = 17/3 x 17/3 x 17/12
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