"Find the maximum value of a rectangular box that can be inscribed in an ellipsoid.." 1. The problem statement, all variables and given/known data Find the maximum value of a rectangular box that can be inscribed in an ellipsoid x^2 /4 + y^2 /64 + z^2 /81 = 1 with sides parallel to the coordinate to the coordinate axes. 2. Relevant equations Lagrange Multiplier method and partial differentiation. 3. The attempt at a solution My attempt is attached as MyWork.jpg. I feel like I should have the correct answer but I did something wrong and I would appreciate it if someone could point out my mistake as well as tell me why it's wrong.