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.

- Write formulas for length, width, and volume of the box, each in terms of `x` .

`l=`functoproc[1000] = 1; vlist[1000]="x"; flist[1000]=""; pts[1000]="2.201,-0.359,-4.839,6.281,-7.199,4.521,-1.839,-1.239,-6.839,1.521,4.161,-2.959,-6.279,6.201,-6.319,6.481,-5.719,7.801,0.001,7.841";

`w=`functoproc[1001] = 1; vlist[1001]="x"; flist[1001]=""; pts[1001]="9.601,0.081,-8.279,6.281,-3.079,4.881,0.521,-0.239,1.081,-6.079,1.681,2.561,5.521,9.161,0.040999999999999,9.961,5.441,0.321,-7.279,-2.479";

`h=`functoproc[1002] = 1; vlist[1002]="x"; flist[1002]=""; pts[1002]="-3.519,-9.399,5.721,-4.359,4.881,4.841,3.801,6.001,-6.599,9.841,4.121,5.241,3.721,-9.959,-4.599,2.121,-6.159,2.041,-8.839,5.481";

`V=`functoproc[1003] = 1; vlist[1003]="x"; flist[1003]=""; pts[1003]="-7.039,-0.639,-4.559,2.441,-8.239,9.241,5.521,6.321,0.121,4.361,2.641,-6.439,9.521,9.681,-9.639,2.721,-3.759,-1.799,4.521,3.121"; - 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 calctoproc[1004] = 1; calcformat[1004] = ''; calctoproc[1007] = 1; calcformat[1007] = ''; 0.5 to 1.5 in calctoproc[1005] = 1; calcformat[1005] = ''; calctoproc[1008] = 1; calcformat[1008] = ''; 1 to 4 in calctoproc[1006] = 1; calcformat[1006] = ''; calctoproc[1009] = 1; calcformat[1009] = '';

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=`calctoproc[1010] = 1; calcformat[1010] = ''; `* Delta x` .