Question: (a) Find all critical points of f(x) = x4 + ax2 + b.
(b) Under what conditions on a and b does this function have exactly one critical point? What is the one critical point, and is it a local maximum, a local minimum, or neither?
(c) Under what conditions on a and b does this function have exactly three critical points? What are they? Which are local maxima and which are local minima?
(d) Is it ever possible for this function to have two critical points? No critical points? More than three critical points? Give an explanation in each case.