Assignment:
An open top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and then folding up the flaps. Let x denote the length of each side of the square to be cut out.
Find the function V that represents the volume of the box in terms of x. Show and explain the answer, and also graph this function.
Using the graph what is the value of x that will produce the maximum volume?
Provide complete and step by step solution for the question and show calculations and use formulas.