2construct a rational function that will solve the problem. then, use a calculator to answer the question.

an open box with a square base is to have a volume of 500 cubic inches. find the dimensions of the box that will have

minimum surface area. let x = length of the side of the base.

show your work:

Dimension of box:-

Side of square base = 10 in

Height of box = 5 in

Minimum Surface area, S = 300 in²

Step-by-step explanation:

An open box with a square base is to have a volume of 500 cubic inches.

Let side of the base be x and height of the box is y

Volume of box = area of base × height

Therefore,

It is open box. The surface area of box, S .

Put  

This would be rational function of surface area.

For maximum/minimum to differentiate S(x)

For critical point, S'(x)=0

Put x = 10 into

y = 5

Double derivative of S(x)

at x = 10

Therefore, Surface is minimum at x = 10 inches

Minimum Surface area, S = 300 in²

a

step-by-step explanation:

a