Question

Minimum surface area box: All boxes with a square base and a volume of 50ft^3 have a surface area given by S(x)=2x^2+200/x, where x is the length of the sides of the base. Find the absoulte minimum of the surface area function. What are the dimensions of the box with minimum surface area?

Answer 1

take the derivative of the surface area function.
dS/dx = 4x - 200/(x^2)

Set it equal to 0 because that is where extrema occur
0 = 4x -200/(x^2)
200 = 4x^3
50 = x^3
x = 3.68

Answer 2

Thank you so much!