An Open Box Is to Be Made from a Square $V ( x ) = x ( 24 - 2 x ) ^ { 2 }$

Multiple Choice

An open box is to be made from a square piece of cardboard, 24 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below) .If the volume of the box is represented by $V ( x ) = x ( 24 - 2 x ) ^ { 2 }$ , determine the domain of $$V ( x )$$ .

A) $D = \{ x \mid x > 0 \}$
B) $D = \{ x \mid 0 < x < 12 \}$
C) $D = \{ x \mid 48 < x < 96 \}$
D) $D = \{ x \mid 0 < x < 24 \}$
E) $D = \{ x \mid 12 < x < 24 \}$