Question 14. (4 points) Suppose a population of deer is susceptible to some disease. Let N (t) denote the number of deer infected after 15 weeks. Suppose the following function models the Spread of infection in this population, for t 2 0 weeks: N(t) = 120t2t'31'2t a) Find the derivative N' (t) You do not need to simplify your answer. b) Within the rst 5 weeks (i.e. the time interval 0 S t g 5), nd the number of weeks If at which N (t) attains a global maximum. Show ALL your work and justify why this is when a GLOBAL maximum is attained. c) What is the global maximum value of N (t) in the time interval [0, 5]