Solve the Problem $x$ Inches on a Side, the Volume of the Box (In

Multiple Choice

Solve the problem.
-An open-top box is to be made by cutting small identical squares from each corner of a 12-by-12-in. sheet of tin and bending up the sides. If each corner square is $x$ inches on a side, the volume of the box (in in. ${ }^{3}$ ) is given by:
$$\mathrm{V}(\mathrm{x}) =144 \mathrm{x}-48 \mathrm{x}^{2}+4 \mathrm{x}^{3}$$
By sketching the graph of $\mathrm{V}(\mathrm{x})$ , estimate the value of $\mathrm{x}$ that maximizes the volume of the box.

A) 1.5 in.
B) 2 in.
C) 6 in.
D) 3 in.