area calculus derivative

Question

An open box is to be made out of a 12-inch by 20-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.

dimensions of box?

height of box?

Answer 1

The box will have dimensions: 20-2x, 12-2x and x.

The volume will be the product of these 3 factors.

The maximum volume will occur when the derivative of the volume function with respect to x is set to 0 and solved for x.

Good luck!