The diagram shows a plan for a rectangular piece of land ABCD. AD = 40 metres. Vegetables

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The diagram shows a plan for a rectangular piece of land ABCD. AD = 40 metres. Vegetables are going to be planted in the triangular vegetable patch ACP. BP = CD= x metres.


a) Show that the area, A m² of the vegetable patch is given by
A = 20x −1/2x2.


b) Given that x can vary, find the maximum area of the vegetable patch,
showing clearly that A is a maximum not a minimum.


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