Aclosed rectangular box with a sqaure
basehas a volume of 64 cubic inches. find the dimensions that give
theminimum surface area.?

  4 inches on each edge of the cube

Step-by-step explanation:

A closed box will have minimum area when it is a cube. For a volume of 64 in^3, the edge length must be ∛64 = 4 inches.

Using derivatives, the base edge length can be defined as x, and the surface area as ...

  S = 2x^2 + 4x(64/x^2)

This is minimized when dS/dx = 0:

  dS/dx =- 4x -256/x^2 = 0

  x^3 = 64

  x = ∛64 = 4 . . . . . should look familiar