An open box of maximum volume is to be made from a square piece of material, 36 inches on a side, by cutting equal squar

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An Open Box Of Maximum Volume Is To Be Made From A Square Piece Of Material 36 Inches On A Side By Cutting Equal Squar 1 (20.75 KiB) Viewed 62 times

An open box of maximum volume is to be made from a square piece of material, 36 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure). (a) Analyticaty complete six rows of a table such as the one below. (The first two rows are shown.) Length and With 36-2(1) Heightx 1 2 3 4 5 6 V= 36-2(3) 36-2(4) 36-3(5) 36-2(5) (D) Write the volume V as a function of 0<x< 18 Use the table to guess the maximum volume. V= Volume V 1116-2(1)1¹-1156 236-2(23) 2048 36-231- 436-2(4)²- 3130 336-253-3340 6[36-2(6)3456 (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 maximam volume from the graph V 3500