calculus
posted by james .
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?

let x be cut size. sides are thus 332x
v = x(332x)^2
v = 4x^3  132x^2 + 1089x
dv/dx = 12x^2  264x + 1089
max/min volume when dv/dx = 0
(2x11)(2x33) = 0
I'll let you figure out which root makes sense.