A designer is creating various open-top boxes by cutting four equally-sized squares from the corners of a standard sheet of 8.5 inch by 11 inch paper, and then folding up and securing the resulting 'flaps' to be the sides of the box.

Let x represent the varying side length of the square cutouts in inches. Let l,w, and h represent the varying length, width and height of the box (in inches), respectively. Note that the width and length dimensions are such that w < l . Let V represent the varying volume of the box in cubic inches.

1. Write formulas for length, width, and volume of the box, each in terms of x .
l=
w=
h=
V=

2. Given the following starting and ending values of x , find the change in x and the resulting change in l .
 x changes from ... Delta x Delta l 0 to 0.5 in 0.5 to 1.5 in 1 to 4 in

Does l change at a constant rate with respect to x ? If yes, enter the appropriate value to complete the statement. If no, enter "DNE".
Delta l= * Delta x .