3. (Strogatz 10.1.11) Consider the map xn+1 = 3xn — x - (a) Find all the fixed points and classify their stability. (b) Draw a cobweb starting at x0 = 1.9. You may want to graph the function on a computer and draw your cobweb on a printout OR numerically calculate some points in the orbit to make sure that your cobweb is reasonably accurate. (c) Draw a cobweb starting at x0 = 2.1. You may want to graph the function on a computer and draw your cobweb on a printout OR numerically calculate some points in the orbit to make sure that your cobweb is reasonably accurate. (d) Show that if |x| ≤ 2, then |f(x)| ≤ 2, where f(x) = 3x - x³. Then show that if |x| > 2, |ƒ(x)| > |x|. Use this to explain the behavior you saw in parts (b) and (c).