A box is to be made out of a 12 cm by 16 cm piece of cardboard. Squares of side length x 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.

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A box is to be made out of a 12 cm by 16 cm piece of cardboard. Squares of side length x 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 V of the box as a function of x. V= _________cm3

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

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

L =______ cm

W = _____cm

H = _____cm

(d) The maximum volume of the box _______is cm3.

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