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Unformatted text preview: may use the backs of these pages for your extra work. You have 50 minutes. Problem 1 (20 points) A company makes a product. It costs 10 dollars to make one item. If it charges 30 dollars per item it will sell exactly 1 , 000 items; but if it charges 20 per item it will sell exactly 2 , 000 items. Assuming a linear demand function, how many items should the company make to maximize its proﬁt. Problem 2 (20 points) f ( x ) is a function whose derivative is √ x 2 + 1. What is the derivative of f (3 x + 2). Problem 3 (20 points) y and z are functions of x with the property z 3 y 5 + z 5 y 7 = 2. Also, when x = 3 we have y = 1 and z = 1. Also, when x = 3, we have dy dx = 5. Find dz dx when x = 3. Problem 4 (20 points) Solve for x . (your answers can involve e and/or ln) (a) (10 points) e (3 x +2) = 5 (b) (10 points) ln (3 x 2 ) = 5 Problem 5 (20 points) Find the derivative of ( x 2 + 1) x...
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 Fall '11
 Nitsche
 Calculus, Derivative, 50 Minutes, 10 dollars, 30 dollars

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