An open box of maximum volume is to be made from a square piece of material,...

 

 

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An open box of maximum volume is to be made from a square piece of material, s = 24 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). 1 x -s-2x+ x (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Height, x Volume, V Width 1 24 - 2(1) 1[24 2(1)]2484 2 24-2(2) - 2[24 2(2)]2800 3 24-2(3) 3[24-2(3)] = 4 24-2(4) 4[24-2(4)] = 5 24-2(5) 5[24 - 2(5)] = 6 24-2(6) 6[24-2(6)]2 = Use the table to guess the maximum volume. V= (b) Write the volume V as a function of x. 0 An open box of maximum volume is to be made from a square piece of material, s = 24 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). 1 x -s-2x+ x (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Height, x Volume, V Width 1 24 - 2(1) 1[24 2(1)]2484 2 24-2(2) - 2[24 2(2)]2800 3 24-2(3) 3[24-2(3)] = 4 24-2(4) 4[24-2(4)] = 5 24-2(5) 5[24 - 2(5)] = 6 24-2(6) 6[24-2(6)]2 = Use the table to guess the maximum volume. V= (b) Write the volume V as a function of x. 0