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Unformatted text preview: Math 2250 Exam #3 Practice Problem Solutions 1. Determine the absolute maximum and minimum values of the function f ( x ) = x 1 + x 2 . Answer: Notice that f is defined for all x . Also, lim x f ( x ) = lim x x 1 + x 2 = 0 , so f doesnt go off to infinity. Now, to find the critical points, compute f ( x ) = (1 + x 2 )(1)- x (2 x ) (1 + x 2 ) 2 = 1- x 2 (1 + x 2 ) 2 , which equals zero precisely when x 2 = 1, or x = 1. Thus, we just need to evaluate f at the critical points: f (1) = 1 2 f (- 1) =- 1 2 Since f limits to 0 in both directions, we see that these are the absolute maximum and absolute minimum values of the function. 2. A specialty publisher has typically sold trade paperbacks for $15, averaging 300 sales per week. The publisher has found that increasing the price by 50 cents reduces sales by 10 per week, so the demand function is p ( x ) =- x 20 + 30. If the books cost $10 each to make, what price should the publisher charge to maximize profit?...
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