A box is constructed from a square piece cardboard with sides of 4 feet by cutting equal squares from the corners and folding up the sides as shown. The volume of the box is given by: V = 4x3 – 16x² + 16x. It is determined that the volume will be at a maximum if the cut-out squares have sides of ÷ft. Is this correct? Explain why or why not. Show ALL your work to support your answer.

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