Instructions: the exam is closed book and closed notes. You may use an approved calculator, but be sure to show your work on each problem for full credit. Work that is crossed out or erased will not be graded. Turn in any scratch paper that you use during the exam. You will have two hours to work on the exam. 5 ht(k ht), (a) find all equilibria. For what values of k is there more than one equilibrium that makes biological sense? (b) for each equilibrium, use the stability theorem/criterion to determine the values of k for which that equilibrium is stable. Show clearly how you are using the stability. 2: (14 points) (a) consider the function f (x) = x2e x, find all critical points of f (x), determine the global maximum and global minimum of f (x) on the interval [ 1, 5].