The area of a rectangle is given by A = length * width. width of the given rectangle is x height is y = 2 - x^2 Area = x(2 - x^2) = 2x - x^3 For area to be maximum, dA/dx = 0 dA/dx = 2 - 3x^2 = 0 3x^2 = 2 x^2 = 2/3 x = √(2/3) y = 2 - (√(2/3))² = 2 - 2/3 = 4/3
Therefore, the required rectangle has a width of 2√(2/3) ≈ 1.63 and a height of 4/3 ≈ 1.33