Problem 1. This problem included material from Sections 4.2 and 4.1. The pathogenesis function f(2') : ~t(t 21)(f +1) is used to model the development of a disease. Where r. from the interval [0.21], represents the number of days in the course of the disease. and f (t) is the number of infected cells per mL of plasma. (a) Calculate the derivatives f'(t) f"(f) and use them to find any critical and inflec tion points for f (t) in the interval [0. 21]. Then use the obtained information to sketch an accurate graph of f(z') over that interval. (hi According to the model using: the function f (1'). What is the peak infection time