An open box is to be made from a square piece of cardboard, $66 \text { inches }$ on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).After determining the function V, in terms of x, that represents the volume of the box, use a graphing utility to estimate the dimensions that will maximize its volume.
A) $22 ^ { \prime \prime } \times 22 ^ { \prime \prime } \times 11 ^ { \prime \prime }$
B) $44 ^ { \prime \prime } \times 44 ^ { \prime \prime } \times 11 ^ { \prime \prime }$
C) $44 ^ { \prime \prime } \times 44 ^ { \prime \prime } \times 22 ^ { \prime \prime }$
D) $33 ^ { \prime \prime } \times 33 ^ { \prime \prime } \times 22 ^ { \prime \prime }$
E) $11 ^ { \prime \prime } \times 11 ^ { \prime \prime } \times 5.5 ^ { \prime \prime }$

Question

An open box is to be made from a square piece of cardboard, $66 \text { inches }$ on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).After determining the function V, in terms of x, that represents the volume of the box, use a graphing utility to estimate the dimensions that will maximize its volume.  
A) $22 ^ { \prime \prime } \times 22 ^ { \prime \prime } \times 11 ^ { \prime \prime }$ 
B) $44 ^ { \prime \prime } \times 44 ^ { \prime \prime } \times 11 ^ { \prime \prime }$ 
C) $44 ^ { \prime \prime } \times 44 ^ { \prime \prime } \times 22 ^ { \prime \prime }$ 
D) $33 ^ { \prime \prime } \times 33 ^ { \prime \prime } \times 22 ^ { \prime \prime }$ 
E) $11 ^ { \prime \prime } \times 11 ^ { \prime \prime } \times 5.5 ^ { \prime \prime }$

Quizplus · Accepted Answer

The Answer of An open box is to be made from a square piece of cardboard, $66 \text { inches }$ on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).After determining the function V, in terms of x, that represents the volume of the box, use a graphing utility to estimate the dimensions that will maximize its volume.  
A) $22 ^ { \prime \prime } \times 22 ^ { \prime \prime } \times 11 ^ { \prime \prime }$ 
B) $44 ^ { \prime \prime } \times 44 ^ { \prime \prime } \times 11 ^ { \prime \prime }$ 
C) $44 ^ { \prime \prime } \times 44 ^ { \prime \prime } \times 22 ^ { \prime \prime }$ 
D) $33 ^ { \prime \prime } \times 33 ^ { \prime \prime } \times 22 ^ { \prime \prime }$ 
E) $11 ^ { \prime \prime } \times 11 ^ { \prime \prime } \times 5.5 ^ { \prime \prime }$

An Open Box Is to Be Made from a Square 66 inches 66 \text { inches }66 inches

An Open Box Is to Be Made from a Square $66 \text { inches }$