A box is to be made out of a 12 cm by 18 cm piece of cardboard. Squares of side length cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top. (a) Express the volume of the box as a function of .

(b) Give the domain of in interval notation. (Use the fact that length and volume must be positive.)

(c) Find the length , width , and height of the resulting box that maximizes the volume. (Assume that ).

= cm

= cm

= cm

(d) The maximum volume of the box is .

i found the equation and set the first derivative equal to zero and solved for x then plugging that number x into the original equation i found to get the max volume.

any help with finding the L, W, and H and the domain would be great.

thank you