An open box is formed from a piece of cardboard 12 inches square by cutting equal squares out of the corners and turning up the sides. Find the volume of the largest box that can be made.

Question

Help!

Answer 1

let x be the edge length of the corner squares

the volume of the box is
... v = x (12 - 2x)^2
... v = 144 x - 48 x^2 + 4 x^3

the 1st derivative will show the maxima/minima

plug in the values to find the volume