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2 Optimization Problems (12.5 points) For the following real valued functions, find their associated minimum * and the minimal value p*, if they exist. Is r* unique? 1. f1 : (a, b) -> R with fi(x) = r 2. f2 : R -+ R with f2(x) = c. cos(x) c30 3. f3 : [0, 2x] -> R with fs(x) = sin(x) 4. f4 : [0, 2x] -> R with fA(x) = sin(2) 5. fs : R -+ R with fs(x) = r - 3r