t is unstable, stable i.s.L., asymptotically stable, or exponentially stable.

    </exercise>

    <exercise><h1>Basin of Attraction and Bifurcation Diagram</h1>

      Consider the first-order system with polynomial dynamics $$\dot x = f(x) = - x^3 + 4x^2 +11x - 30.$$

      <ol type="a">

        <li> Sketch the graph of the function $f(x)$, and identify all the equilibrium points.  (Feel free to plot this with a tool of your choice to check your work.)</li>

        <li> For each equilibrium point, dete