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 what values of $\mathrm{x}$ result in a box with a volume greater than $64 \mathrm{in}^{3}$ .

A) 1.5 in. $\leq x \leq 2.5$ in.
B) 0.1 in. $\leq x \leq 5.0$ in.
C) 1.0 in. $\leq x \leq 3.0$ in.
D) 0.54 in. $\leq x \leq 4$ in.