Well, for starters take the first derivative so you can see where the polynomial's critical points are.

The roots of this function are the extrema of the original function. That is, set and solve (hint recognize that 0 must be a root, so to find others, solve .)

Take the next derivative and substitute in the critical points found above. If the result is negative then it's a max. If it's positive then it's a min. If it equals zero, then the point is neither max or min (throw it out),unlessthe whole original function is constant, which it is not in this case.