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Unformatted text preview: T T T F F F F Q T T F F T T F F R (P Q) (R R) [ R (P Q)] R T T T F T T T T T F T T T T T F T T T T T F T T Therefore, the two propositional forms are equivalet. 3 Section C: Analytical Choose 5 of the following 6 questions. This section of the exam is worth 50%. 1. Consider the function: defined over x (0, 15). f (x) = x12 15 - x 14 2 (a) Calculate the first derivative. (c) Is the function strictly concave, strictly convex, or neither? (Be sure to clearly explain your answer.) (b) Calculate the second derivative. Solution: (d) Does a global maximum exist over the domain (0, 15)? If so find it. (a) The first derivative is: 1 15 - x 14 1 12 15 - x -34 f (x) = x-12 - x 2 2 8 2 (b) The second derivative is: 2. For each of the following functions, (i) compute the first derivative, (ii) compute the second derivative, (iii) indicate whether the function is strictly concave, strictly convex, or neither (explain your reasoning), (iv) indicate whether it is homogeneous or not. (a) f (x) = x2 + 2 (b) f (x) = ln x + 5 (d) f (x) = 1 (c) f (x) = (x2 + x3 - 1)2 (d) The global maximum is x = 10. (c) Since for all x (0, 15), f (x) < 0, the function is st...
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This document was uploaded on 03/20/2014 for the course ECON 2p30 at Brock University, Canada.
- Fall '12