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]="4.321,3.321,2.721,7.721,-2.719,2.601,4.921,-3.999,-6.439,9.521,-6.839,-2.919,-4.719,4.921,0.401,-8.279,-8.879,0.961,-1.919,7.481";

`w=`functoproc[1001] = 1; vlist[1001]="x"; flist[1001]=""; pts[1001]="4.801,0.161,-0.399,-9.599,-0.999,-8.799,-9.719,4.921,6.441,2.441,-2.959,-2.679,6.681,-3.079,6.641,7.001,9.521,-2.719,-2.479,3.801";

`h=`functoproc[1002] = 1; vlist[1002]="x"; flist[1002]=""; pts[1002]="-9.479,5.961,9.921,0.441,4.521,-6.719,-5.639,3.441,5.241,1.641,-5.319,3.121,-5.519,6.881,-1.999,-2.559,-9.439,4.641,-5.639,1.681";

`V=`functoproc[1003] = 1; vlist[1003]="x"; flist[1003]=""; pts[1003]="8.441,-1.559,4.281,-6.119,-6.119,-2.439,-0.119,-7.079,-4.839,9.201,7.601,5.961,2.161,1.121,5.881,2.161,3.921,-0.079,6.881,-3.959"; - 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` .