In a hospital, a drug is given to a patient. Let f(t) be the amount of drug (in mg) in the patient's body t minutes after it is administered. The nurses want to predict how the body will absorb the drug (the shape of the graph y = f(t)) to be able to prepare the next course of action. One of them remembers about Taylor polynomials from their Calculus course and explains that they allow to predict the shape of a function by making very accurate measurements of the function at one point. They decide to do this and they find the following details about the patient's absorption of the drug: . f(15) = 147 . f' (15) = _ 16 10 . f" (15) = 11 1 000 Use these details to approximate the average amount of drug in the patient's body over the first 2 hours: 1 120 f(t) dt 120 Jo