A rectangular piece of cardboard, 40 in. long by in. wide is used for making a rectangular box (open top) by cutting out squares of x by x from the corners and folding up the sides.

(a) Create a polynomial expression for the volume Vin terms of x.
(b) Make a plot of V versus x.
(c) Determine x if the volume of the box is 1,000 in.3.
(d) Determine the value of x that corresponds to the box with the largest possible volume, and determine that volume.

Transcribed Image Text:

40 in. 22 in.