Problem 1. Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = xy subject to constraint o' + y' = 1 Problem 2. Find the first four terms of the Taylor series for the function f(x) = -1/2 about a=4.Problem 3. Medical researchers are examining the effects of a drug in treating a particular disease. Let the function P = f(w, t) give the probability P (in percent) that the patient will die, where the patient's weight is w (in pounds) and the patient has been using the drug for t years. wt 0 1 2 3 4 5 6 150 0.63 0.45 0.34 0.25 0.18 0.11 0.04 160 0.67 0.49 0.37 0.28 0.20 0.13 0.07 170 0.72 0.52 0.40 0.31 0.23 0.16 0.10 180 0.76 0.56 0.44 0.34 0.26 0.19 0.12 190 0.81 0.60 0.47 0.37 0.29 0.22 0.15 200 0.85 0.63 0.50 0.40 0.32 0.24 0.18 210 0.90 0.67 0.53 0.43 0.35 0.27 0.20 220 0.94 0.71 0.57 0.46 0.37 0.30 0.23 Approximate Vf (170, 5) and provide a general explanation of what V f (170, 5) means in context of this situation