Posted by james on .
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?

calculus 
Steve,
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.