You must show your work if you wish to receive credit or partial credit. You have 50 minutes to nish this exam. 7 pages for questions and 1 page for scratch paper. 1: (35 pts) let f (x) = x2. 1 + x2 , x r: determine where f (x) is increasing and decreasing. Find all local maxima and minima of f (x): determine where f (x) is concave up and concave down. 2: (cont. ) c) find and lim x f (x) lim x f (x) then determine whether f (x) has horizontal asymptotes, sketch the graph of f (x) together with its local extrema, asymptotes and in ection points (if exist). Determine the global maxima and minima of f (x). 3: (15 pts) a) denote the population size at time t by n (t), which is continuous on 0 t 3 and di erentiable on 0 < t < 3.
