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Use differential calculus to find the maximum/minimum for an engineering problem. A sheet of metal is...

Use differential calculus to find the maximum/minimum for an engineering problem.

A sheet of metal is 340 mm x 225 mm and has four equal squares cut out at the corners so that the sides and edges can be turned up to form an open topped box shape.

Calculate: (a) The lengths of the sides of the cut-out squares for the volume of the box to be as big as possible.

(b) The maximum volume of the box.

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