(a) A square piece of cardboard 36 centimeters on a side is to be formed into a...

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(a) A square piece of cardboard 36 centimeters on a side is to be formed into a rectangular box by cutting squares with length x from each corner and folding up the sides. What is the maximum
volume possible for the box?
(b) Show that if the piece of cardboard is k centimeters on each side, cutting squares of size k 6 and folding up the sides gives the maximum volume.
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