An open box is to be made from a square piece of cardboard, 36 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) $12 ^ {||}$ × $12 ^ { ||}$ × $6^{||}$
B) $24^{||}$ × $24^{||}$ × $6^{||}$
C) $24^{||}$ × $24^{||}$ × $12 ^ { || }$
D) $18^ { ||}$ × $18^ { ||}$ × $12^ { ||}$
E) $6^ { ||}$ × $6^ { ||}$ × $3^ { ||}$

Question

An open box is to be made from a square piece of cardboard, 36 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) $12 ^ {||}$ × $12 ^ { ||}$ × $6^{||}$ 
B) $24^{||}$ × $24^{||}$ × $6^{||}$ 
C) $24^{||}$ × $24^{||}$ × $12 ^ { || }$ 
D) $18^ { ||}$ × $18^ { ||}$ × $12^ { ||}$ 
E) $6^ { ||}$ × $6^ { ||}$ × $3^ { ||}$

Quizplus · Accepted Answer

The Answer of An open box is to be made from a square piece of cardboard, 36 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) $12 ^ {||}$ × $12 ^ { ||}$ × $6^{||}$ 
B) $24^{||}$ × $24^{||}$ × $6^{||}$ 
C) $24^{||}$ × $24^{||}$ × $12 ^ { || }$ 
D) $18^ { ||}$ × $18^ { ||}$ × $12^ { ||}$ 
E) $6^ { ||}$ × $6^ { ||}$ × $3^ { ||}$

An Open Box Is to Be Made from a Square 12∣∣12 ^ {||}12∣∣

An Open Box Is to Be Made from a Square $12 ^ {||}$