1: A patient takes vitamin pills daily. Each day he must have at least 240 IU of vitamin A, 5 mg of vitamin B1, and 120 mg of vitamin C. He can choose between pill 1, which contains 120 IU of vitamin A, 1 mg of vitamin B1, and 15 mg of vitamin C; and pill 2, which contains 30 IU of vitamin A, 1 mg of vitamin B 1, and 40 mg of vitamin C. Pill 1 costs $0.10, and pill 2 costs $0.20. Using Python, determine how many of each pill he should take daily in order to minimize cost and determine the minimum cost. Also, determine the amount of surplus of each type of vitamin, if any. QUESTION 2: The following is a graph of a third degree polynomial with leading coefficient 1. Determine the function depicted in the graph. Using Python, recreate the graph of the original function, f ( x ) , as well as the graph of its derivative. QUESTION 3 The average number of vehicles waiting in line to enter a parking ramp can be modeled by the function 2 f ( x )= x 2(1x ) where x is a quantity between 0 and 1 known as the traffic intensity. Find the rate of change of the number of vehicles in line with respect to the traffic intensity for x = 0.3. QUESTION 4: Using data in a car magazine, we constructed the mathematical model 0.0482t y=100 e for the percentage of cars of a certain type still on the road after t years. Using Python, determine the rate of change of the percent of cars still on the road after 5 years. QUESTION 5: For the following function, determine the domain, critical points, intervals where the function is increasing or decreasing, inflection points, intervals of concavity, intercepts, and asymptotes where applicable. Use this information to graph the function. f ( x )=5 x 15 x QUESTION 6: For a certain drug, the rate of reaction in appropriate units is given by R ' ( t )= where t 3 5 + t+1 t +1 is time (in hours) after the drug is administered. Find the total reaction to the drug from 8 to 24 hours after it is administered. QUESTION 7: The time between goals (in minutes) for a professional soccer team during a recent season can be approximated by x f ( x )= 1 85 e 85 Using Python determine the (separate) probabilities that the time for a goal is no more than 68 minutes, and 457 minutes or more