How do I derive the critical points of the 2nd derivative so that I can graph this function [f(x)=(x^2-1)^3]?

You mean f(x) = (-x^2 - x - 2)/(x - 2), I imagine. PLEASE read "order of operations" in Wikipedia. Anyway, the graph will have a vertical asymptote at x = 2; it's simple enough to plug in some numbers to get the points (3,-17), (4,-13), (6,-12.5), (10,-15.9) which will all be connected; and the points (1,5), (0,1), (-1,1/3), (-2,1/2), (-4,5/3), which will also all be connected; but note that nothing connects across the vertical line x=2.

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