''Solution'': ''g(x,y) = x<sup>2</sup> + y<sup>2</sup> - 2 = 0''. We want to maximize the area of a rectangle. Assuming symmetry about the origin (we could always map a solution to a symmetric one), the area ''f(x,y)'' that we want to maximize equals 2x times 2y: ''f(x,y) = 4xy''. From the equation for the Lagrangian multiplier above, and setting the ''x'' and ''y'' coefficients equal to each other, we can generate these two equations: | ''Solution'': ''g(x,y) = x<sup>2</sup> + y<sup>2</sup> - 2 = 0''. We want to maximize the area of a rectangle. Assuming symmetry about the origin (we could always map a solution to a symmetric one), the area ''f(x,y)'' that we want to maximize equals 2x times 2y: ''f(x,y) = 4xy''. From the equation for the Lagrangian multiplier above, and setting the ''x'' and ''y'' coefficients equal to each other, we can generate these two equations: |