Consider the system x' = rx + x3 - x5​, which exhibits a pitchfork bifurcation.

a. Find the algebraic expressions for all teh fixed points as r varies

b. Sketch the vector fields as r varies. Be sure to indicate all the fixed points and their stability

c. Calculate rs​, the parameter value at whcih the nonzero fixed points are born in a saddle-node bifurcation