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Amongst all pairs of positive number with sum 24, find those whose product is maximum |
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Answer» Let the number be x and `(24 -x)` Let `P = x (24 -x) = (24 x - x^(2))` then, `(dP)/(dx) = (24 - 2x) and (d^(2)P)/(dx^(2)) = -2` Now, `(dP)/(dx) = 0 rArr (24 - 2x) = 0 rArr x = 12` Thus, `{(d^(2)P)/(dx^(2))}_(x = 12) = -2 lt 0` `:. x = 12`, is point of maximum Hence, the required number are 12 and 12 |
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