An Open-Top Box Is to Be Made by Cutting Small $V ( x ) = 144 x - 48 x ^ { 2 } + 4 x ^ { 3 }$

Multiple Choice

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 $V ( x ) = 144 x - 48 x ^ { 2 } + 4 x ^ { 3 }$ . By sketching the graph of V(x) , estimate what values of x result in a box with a volume greater than 64 in³ .

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