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An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of each side of the square to be cut out.
The dimensions of the box will be (4-2x) by (6-2x) by x
a) Find the function V that represents the volume of the box in terms of x.
V = (4-2x)*(6-2x)*x
V = 4x^3 - 20x^2 + 24x
b) Graph this function and show the graph over the valid range of the variable x..
c) Using the graph, what is the value of x that will produce the maximum volume?
It is about .8 ft or about 9.6 inches.
Max vol would be 2.4 * 4.4 * .8 = 8.45 cu ft