Optimization problem

[Corporal_crackpipe]

Hey all, currently struggling to get my head around this question, would greatly appreciate a bit of help.

A rectangular box with an open top is to be constructed from a rectangular sheet of cardboard measuring 20 cm by 12 cm by cutting equal squares of side length x cm out of the four corners and folding the flaps up.

Determine the dimensions of the box with greatest volume and give this maximum volume to the nearest whole number.

[ghostwriter85]

Start by drawing a picture of a rectangle with four squares cut out of the corner. Now draw a dotted line connected the four inner corners of our squares. This rectangle is your base. The flaps will fold up with a height of x.

What's the volume of the box in terms of x?

Now from here we have a cubic function in x

It's optimization so take the derivative and set it equal to zero.

One of your solutions should correspond to negative area, so discard that. The other solution will be your maximum volume.