# a side, by cutting equal squares from the An open box of maximum volume is to be made from a square piece of material, s = 36 inches on corners and turning up the sides (see figure). S-2r- T X shown.) (a) Analytically complete six rows of a table such as the one below. (The first two rows are Length and Width Volume, V Height, x 1[36 2(1)]2 2(1) 1156 36 1 2[36 2(2)]2 2(2) = 2048 36 3[36 2(3)]2 36 2(3) 3 4[36 2(4)]2 = 36 2(4) 2(5) 5[36 2(5)]2 = 36 36 2(6) 6[36 2(6)12 - Use the table to guess the maximum volume. V= (b) Write the volume V as a function of x. 0 x< 18 V= c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V = (d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V V 3500 400 3000 2500 300 2000 200 1500 1000 100 500 X X 15 4 10 2 V V 3500 1500 3000 2500 1000 2000 1500 500 1000 500 X 15 10 15 10 st

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Which is the result? help_outlineImage Transcriptionclosea side, by cutting equal squares from the An open box of maximum volume is to be made from a square piece of material, s = 36 inches on corners and turning up the sides (see figure). S-2r- T X shown.) (a) Analytically complete six rows of a table such as the one below. (The first two rows are Length and Width Volume, V Height, x 1[36 2(1)]2 2(1) 1156 36 1 2[36 2(2)]2 2(2) = 2048 36 3[36 2(3)]2 36 2(3) 3 4[36 2(4)]2 = 36 2(4) 2(5) 5[36 2(5)]2 = 36 36 2(6) 6[36 2(6)12 - Use the table to guess the maximum volume. V= (b) Write the volume V as a function of x. 0 x< 18 V= c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V = (d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V V 3500 400 3000 2500 300 2000 200 1500 1000 100 500 X X 15 4 10 2 V V 3500 1500 3000 2500 1000 2000 1500 500 1000 500 X 15 10 15 10 st fullscreen

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