a rectangle is inscribed in the upper half of the circle x^2+y^2=a^2 calculate the area of the largest such rectangle.

Question

So A=2xy
y=sqrt(a^2-x^2)A

what do I do from there?

Answer 1

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

Answer 2

the answer is a^2