1. The problem statement, all variables and given/known data Find the dimensions of the rectangle of greatest and least area that can be inscribed in the ellipse x^2/16 + y^2/9 = 1 with sides parallel to the coordinate axes. 3. The attempt at a solution f(x,y) = (2x)(2y) = 4xy ∇f = <4y,4x> ∇g = <x/8,2y/9> ∇f = λ∇g 4y = λx/8 4x = λ2y/9 I can isolate lambda because y=0,x=0 is not a part of the ellipse. λ = 32y/x λ = 18x/y 32y/x = 18x/y x^2 = 16y^2/9 Sub into ellipse 2y^2/9= 1 y = 3/√2 x = 2√2 I don't know what to do after this, I know I am supposed to check whether it is a maximum or not, but I don't know the method. What would the next step be?