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?