Let k E R be a parameter of interest. Consider the fanly of DEs %_ $2+kmk2=f[m;k) In! for all real values of k. {a} Find the critical points 33* as function of 7, and specify for what Ila-values they exist. Hint: use the quadratic formula to factor f. (b) Determine for what values of 15.: each equilibrium 1"\" is stable. Note: if it is not stable, the equilibria is unstable. Hint: Drawing stability diagrams or different F; values is useful here. (c) Determine all bifurcation points 155* where the existence andfor stability of the equilibria points change. (d) Draw a bifurcation diagram with k on the horizontal axis m'{k) on the vertical. Use a solid line to indicate stability and a dashed line to indicate instability