1. an open box is to be made from a rectangular a piece of cardboard of dimension 25 inches by 40 inches. four x by x flaps are formed at each corner of the cardboard, then the ends are turned up and glued together with the flapes to make an open box.(see figure below)
(a) complete the following table.
length of the flap, x: 0,1,2,3,4,5..find width of the box, w, volume of the box, length of the box
(b) write the volume of the box as a function of x
(c) what are the possible values of x?
(d) use a graphing calculator to graph the function. be sure to use an appropriate viewing window. what dimensions will maximize the volume of the box? for what values of x is the volume 1000 cubic inches?