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MATHEMATICS FOR BUSINESS AND ECONOMICS-I (Spring 2022) Quiz II 1. Construct the function f (x) = -x3 + x2 + 5x + 1. Determine critical points, regions where the function is increasing or decreasing, inflection points, regions where the function is concave up or concave down, intercepts where possible. (3 points) 2. A deli sells 640 sandwiches per day at a price of $8 each. A market survey shows that for every $0.10 reduction in price, 40 more sandwiches will be sold. How much should the deli charge for a sandwich in order to maximize revenue (3 points) 3. The revenue and cost (in thousands of dollars) from the manufacture of x thousand specialty cupcakes and y thousand pies are, respectively, R(x, y) = 12xy + 5 - 2x2 and C(x, y) = x2 + 2y3 . How many units of each product will produce the maximum profit? What is the maximum profit? (3.5 points) 4. Find all asymptotes of the function: f (x) = 4 -x (1 point) 5. Find the first-order partial derivatives of z(x; y) = V/2x - y + 12 In (x + y2) at (5; 2). (1.5 points)