4- Show that a Saddle-node bifurcation occurs at a critical value of r, to be determined. Sketch the bifurcation diagram of fixed points x^* versus r.ẋ = r - cosh xShow that a transcritical bifurcation occurs at a critical value of r, to be determined. Sketch the bifurcation diagram of fixed points x^* versus r.ẋ = rx x^2Show that a Pitchfork bifurcation occurs at a critical value of r, to be determined. Sketch the bifurcation diagram of fixed points x^* versus r.ẋ = x (rx)/(1 x^2)