Consider the equation x˙ = (r − x)(r − x 2 ). (a) Sketch a bifurcation diagram for this equation. Identify the unstable and stable fixed points in the diagram with dashed or solid lines, respectively. Clearly label the values of r and x at which the bifurcations occur. Hint for sketching the diagram: the way the equation is factored, you can sketch each factor separately, which is a very reasonable thing to do by hand. (b) Classify the types of bifurcations that occur as saddle node, transcritical, subcritical pitchfork or supercritical pitchfork, or none of these. Briefly explain your reasoning for each.