A lidless box with square ends is to be made from a thin sheet of metal. Determine the least area of the metal used for which the volume of the box is 3.5m^3.
This is my solution:
A = x^2 + 4xh
Substitute h = 3.5/x^2 into A
So A = x^2 + 14x^-1
dA/dx = 2x - 14x^-2
Equating dA/dx = 0, so x = 1.91cm
Therefore, the least area of the metal used = 10.98cm^2