An open box of maximum volume is to be made from a square piece of material, s = 30 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure). 2x S - 2x (a) Analytically complete six rows of the table below. Use the table to guess the maximum volume. (The first two rows are shown.) Height, x Length and Width Volume, V 30 - 2(1) 1[30 - 2(1)]2 = 784 N 30 - 2(2 ) 2[30 - 2(2) ]2 = 1352 m 30 - 2(3) 3[30 - 2(3)]2 = 30 - 2(4 ) 4[30 - 2(4)12 = UT 30 - 2(5 ) 5[30 - 2(5)12 = 30 - 2(6 ) 6[30 - 2(6)12 = (b) Write the volume V as a function of x. V = x(30 - 2x ) 2 (c) Use calculus to find the critical number of the function in part (b). Then find the maximum value. Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. The maximum volume is V =