Using the first and second order derivatives to find the critical points of this function has left me very confused -- they don't mesh at all with the critical points on the graph of the function (as displayed by a graphing calculator).

So, that give potential critical points of x= 1, and -3/2 for relative extremas and x=-2/3 for a point of inflection.

The calculator displays critical points (min, max, min, respectively) of x= 3, 0.6861393, and -2.186138.

Why the discrepancy?