An open box is to be made from a flat square piece of material 20 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 piece of material 20 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:  .I keep getting all real numbers and its saying that it is wrong.

Steve · Answer

v(x) = (20-2x)^2 * x

Of course all real numbers is wrong. The material is only 20 inches square. You cannot include numbers like 500 in the domain. You have to cut two tabs out, so each must be less than 10 in width.

0 <= x <= 10

The base of the box is 20-2x, and must be non-negative in the real world.