Question

A 33 by 33 square piece of cardboard is to be made into a box by cutting out equal square corners from each side of the square. What size corners should be cut out so that the volume of the box is maximized?

Answers

let x be cut size. sides are thus 33-2x

v = x(33-2x)^2
v = 4x^3 - 132x^2 + 1089x

dv/dx = 12x^2 - 264x + 1089

max/min volume when dv/dx = 0
(2x-11)(2x-33) = 0

I'll let you figure out which root makes sense.

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