An open box is to be made from a flat square of material 16 inches in length and width by cutting equal squares of length x from the corners and folding up the sides.

Question

An open box is to be made from a flat square of material 16 inches in length and width by cutting equal squares of length x from the corners and folding up the sides.

a. Write the volume

V of the box as a function of x Leave it as a product of factors, you do not have to multiply out the factors.

V(x) =

b. Give the domain of this volume function in interval notation:

Answer 1

V = (16-2x)(16-2x)(x) = 4x(8-x)(8-x) = 4x(8-x)^2

0 < x < 8 is the domain or (0,8) in interval notation

if x = 0 or 8, there is no box, so don't use brackets, just parentheses.