If 5000 feet of fencing are used to enclose a rectangular field, the resulting area of the field is A=x(2500-x) , where x is the width of the pen. What is the maximum possible area of the pen? A) 62,500ft² B) 1,562,500ft² C) 1250ft² D) 31,250ft²

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Quizplus · Accepted Answer

The area function A=x(2500-x) is a quadratic function, and its maximum value occurs at the vertex. The vertex of a quadratic function ax^2 + bx + c is at x = -b/(2a). Here, a = -1 and b = 2500, so x = 1250. Substituting x = 1250 into the area function gives A = 1250(2500-1250) = 1,562,500 ft².

If 5000 Feet of Fencing Are Used to Enclose a Rectangular