Semistable equilibrium points are rare. Here, we will see why.

a) X = X^2 has an equilibrium point at X = 0. Determine the stability of this equilibrium point.

b) Use graphical methods to find the equilibria of X = (X^2) +a for at least one positive and two negative values of a. For each value of a, determine the stability of the equilibria.

c) Use your findings to explain why semistable equilibria rarely occur in real life.