calculus
posted by jim .
You are planning to make an opentop box from an 12 in by 12 in piece of cardboard
by cutting congruent squares from the corners and folding up the sides.
What are the dimensions (of the 3 sides) of the largest volume you can make this way?

let the size of the cut out squares be x by x inches
so the base of the box is 122x by 122x and its height is x inches.
volume = x(122x^2
expand, then find d(volume)dx
set that equal to zero and solve for x,
from which you can then find the dimensions