Question 83450
An open-top box is to be constructed from a 6 foot by 8 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. 
Dimensions:
Length = 8 - 2x
Width = 6 - 2x
Height = x
a.Find the function V that represents the volume of the box in terms of x.
V(x) = l*w*h = (8 - 2x)(6 - 2x)(x) = 48x - 28x^2 + 4x^3
b.Graph this function and show the graph over the valid range of the variable x.
{{{graph(300,300,-1,5,-6,26,48x - 28x^2 + 4x^3)}}}
c. Using the graph, what is the value of x that will produce the maximum volume?
Seems when x = 1 ... max volume is 24ft^3