6. (7.2) Construct the phase plot for y' = (y - 1)(y + 1)(-y + 3). Identify all of the equilibria and determine whether they are locally stable or unstable. Show your work to construct the phase plot by plugging in values for y between -2 and 4. Note, once you find 3 equilibrium points, there cannot be any more since the degree of y' is 3. 7. (7.2) Suppose a population grows according to the logistic equation but is subject to a constant per capita harvest rate of h > 0. If N(t) is the population size at time t, the population dynamics are dN N dt r(1 KIN - hN Different values of h result in different equilibrium population sizes; if h is large enough, we might expect extinction. (a) Suppose r = 2 and K = 1000. Find all equilibria. (b) What values of h would make the population go extinct? Mathematically, this question is asking which values of h would make the nonzero equilibrium in part (a) unstable, in such a way that the population continues to decrease over time. (c) Suppose r = 2, K = 1000, and h = 2. What can you say about the solution N? (d) Determine the values of h that make the nonzero equilibrium in part (a) locally stable. Assume h * 2