CASE STUDY CHALLENGE

Maxima & Minima: Sports Field Design

In an elliptical sports field, the authority wants to design a rectangular soccer field with the maximum possible area. The sports field is given by the graph of the equation:

x2/a2 + y2/b2 = 1

Rectangular Field

Answer the following:

(i) If the length and breadth of the rectangular soccer field be 2x and 2y respectively, then find the area function A(x) in terms of x. [1]
(ii) Find the critical point(s) of the area function A(x). [1]
(iii) (a) Using first derivative test, find the length 2x and breadth 2y of the soccer field (in terms of a and b) that maximize the area.

— OR —

(b) Using second derivative test, find the length 2x and breadth 2y of the soccer field (in terms of a and b) that maximize the area.

 [2]
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