SOLUTION: from a square sheet of cardboard 8 in by 11 in, square corners are cut out so the sides can be folded up to make a box. what dimensions will yield a box of max. volume?

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Question 940694: from a square sheet of cardboard 8 in by 11 in, square corners are cut out so the sides can be folded up to make a box. what dimensions will yield a box of max. volume?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, length edge for squares to cut.

%288-2x%29%2811-2x%29%2Ax=volume
v%28x%29=%2888-22x-16x%2B4x%5E2%29x
v%28x%29=4x%5E3-38x%5E2%2B88x

DERIVATIVE APPLICATION - dv%2Fdx=0 for max or min volume.

dv%2Fdx=12x%5E2-76x%2B88=0

6x%5E2-38x%2B44=0

3x%5E2-19x%2B22=0

x=%2819%2B-+sqrt%2819%5E2-4%2A3%2A22%29%29%2F%282%2A3%29, one of these will work and the other not.
highlight%28x=%2819-sqrt%2897%29%29%2F6%29----How tall is this box, and the amount of edge to cut from each corner of the cardboard to make the box. For MAXIMUM volume.