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The diagram shows a rectangular enclosure, with a wall forming one side. A rope, of length 20 metres, is used to form the remaining three sides. The width of the enclosure is x metres.
- Show that the enclosed area, \(\mathrm { Am } ^ { 2 }\), is given by
$$A = 20 x - 2 x ^ { 2 } .$$
- Use differentiation to find the maximum value of A .