1. A box without a top is to be made from a rectangular piece of cardboard, with dimensions 3 in. b) in., by cutting out square corners with side length x and folding up the sides.

a) The volume of the box is represented by .

b) A side length of 0.653 inches leads to the maximum volume of the box: 6.299 inches.

Step-by-step explanation:

a) The volume of the box (), in cubic inches, is modelled by the equation for the cuboid:

(1)

Where is the side length of the cutted square corners, in inches.

The volume of the box is represented by .

b) The method consist in graphing the polynomial and looking for a relative maximum. We graph the equation found in a) by means of a graphic tool. We present the outcome in the image attached below. According to this, a side length of 0.653 inches leads to the maximum volume of the box: 6.299 inches.

so what is the problem what are they asking you to solve

step-by-step explanation:

so what is the problem what are they asking you to solve