SOLUTION: 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 the folding up the flaps. Let x denote the length of e

Question 33379: 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 the folding up the flaps. Let x denote the length of each side of the square to be cut out.
a)Find the function V that represents the volume of the box in terms of x.
b)Graph this function.
c)Using the graph, what is the value of x that will produce the maximum volume?

Answer by mukhopadhyay(490) (Show Source): You can put this solution on YOUR website!
The dimension of the rectangular cardboard is 6 ft X 8 ft
Let x-ft be each side of the square cut out from each of the four corners.
The length of the open-top box would be (8-2x) ft (Note: two corners);
The width of the open-top box would be (6-2x) ft.
The height of the open-top box would be x ft. (if you draw a diagram, it will neatly explain the resulting dimension of the open-top box);
The voume of a box = Length X Width X Height;
If V(x) represents the volume function of the box:
V(x) = x(8-2x)(6-2x);
...............
As far as graphing goes, this is a polynomial of degree 3. This is also bound by the restriction (domain of the function) x >= 0 and x <= 3;
.....................
You need a graphing calculator to
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