text: I don't remember that part of Calculus very well but i think that this is the right way of making it.\n\nThe area of the rectangle is 2xy. I multiplied by 2 because xy would only calculate the area of the positive side of x. Since its corners won't go besides the parabola we can use that function  to get y in terms of x in the rectangle. The area of the rectangle will now be 2(x)(12-x^2)\nA = 2x(12-x^2)\nA = 24x-2x^3\nthe derivative of the area is \nA' = 24 - 6x^2\nThe critical points for the area are\n0 = 24 - 6x^2\n6x^2 = 24\nx^2 = 4\nx = 2\nso the biggest area would be A(2) = 24(2) - 2 (2^3)\nA(2) = 48 - 16 = 32