what are the inflection points
F''(x)=(1/2)(8-x^2)(-2x)-[2x(8-x^2)-(2x)(x^2)
the inflection points of F?
if that is what you want, and you are given F'' here, just set F'' = 0 and solve for x. this will give you the points you want to test--your possible inflection points. now plot these points on a number line, and test the intervals between them by plugging in a point in the intervals into F''. if on either side of one of your possible inflection points F'' changes sign, then that point is indeed an inflection point. other wise, it is not.