Arectangle is inscribed in the upper half of the circle x2 y2 = a2 as shown at right. calculate the area of the largest such rectangle.

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Below is the solution, i hope it helps:
A = 2 x (a^2+x^2)^.5 
dA/dx = 2 x (2x)(.5)(a^2+x^2)^-.5) + 2 (a^2+x^2)^.5 

= 0 for max or min