Posted by Anonymous on Friday, April 20, 2012 at 1:31pm.
Take an 8.5 by 14inch piece of paper and cut out four equal squares from the corners. Fold up the sides to create an open box. Find the dimensions of the box that has maximum volume. (Enter your answers as a commaseparated list. Round your answer to three decimal places.)

calculus  Steve, Friday, April 20, 2012 at 2:14pm
cut squares of length x
v = x(8.52x)^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 8.517/6 x 8.517/6 x 17/12 = 17/3 x 17/3 x 17/12
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