1. The problem statement, all variables and given/known data Find the dimensions of the largest rectangle with sides parallel to the axes that can be inscribed in the ellipse x^2 + 4y^2 = 4 2. Relevant equations 3. The attempt at a solution I simplified the equation of the ellipse into the ellipse formula: x^2/4 + y^2 = 1 Then I manipulated the equation to isolate y: y = (sqrt(4-x^2)/2) Then, since the area of the rectangle can be divided into four equal parts with equal length and width, I substituted my y into my area formula, a = 4xy: a = 2x(sqrt(4-x^2)) Now I find the derivative of my area... a' = (8-4x^2)/sqrt(4-x^2) ... Set it equal to 0 to find my maximum value for x: (4(2-x^2))/sqrt(4-x^2) = 0 And find that x is equal to sqrt(2). (which is the right answer, now I just need y) Then, I substituted my value for x back into my area formula (a = 4x(sqrt(4-x^2)/2))) 4(sqrt(2))(sqrt(4-(sqrt(2))^2)/2) and end up with my area as 4. Then I substituted both this area and my x value back into my area formula, a = 4xy: 4 = 4(sqrt(2))y and find that y is equal to 4. However, the back of my book tells me that I should have y = 2sqrt(2). I have looked it over several times and cannot find my mistake. Help would be much appreciated!!