1. The problem statement, all variables and given/known data Determine the dimensions of a rectangular box, open at the top, having volume 4 m3, and requiring the least amount of material for its construction. Use the second partials test. (Hint: Take advantage of the symmetry of the problem.) 2. Relevant equations 3. The attempt at a solution Volume, V= 4m^3 let x = length y = width z = height 4m^3 = xyz x = 4/yz because it is an open at the top rectangular box, the Surface, S = 2xz + 2yz + xy substitute x=4/yz inside the surface equation.. S = 8/y + 2yz + 4/z to find the critical points, take the partial with respect to y and z.. the equal it to zero.. S'(y)= 2z - 8/y^2 S'(z)= 2y - 4/z^2 solve the equations, i get, when y = 0, z = 0.. y = 8, z = 1/16 the problem is, what should i do next?