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

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Calculus

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An open box of maximum volume is to be made from a square piece of material s 36 inches on a side by cutting equal squares from the corners and turning up the sides see figure a Analytically complete six rows of a table such as the one below The first two rows are shown Height x Length and Volume V Width 362 1 36 2 2 3 36 2 3 3 36 2 3 362 4 4 36 2 4 362 5 5 36 2 5 2 362 6 6 36 2 6 12 1 2 V 4 5 6 s 2r 1 362 1 2 1156 2 362 2 2 2048 Use the table to guess the maximum volume V b Write the volume V as a function of x 0 x 18 E c Use calculus to find the critical number of the f

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