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6. (20 points) Sketch the graph of a single function f (x) which satisfies all of the following conditions. Give the intervals of increase, decrease, and concavity. Label (on the graph) all local maxima and minima, points of inflection, and asymptotes. (i) f (x) is defined for all real numbers except for x = 0. (ii) f' ( x ) = 3(4-3x) x3 (iii) f" (x ) = 18(x - 2) (iv) lim f(x) = 2 X - -00 (v) lim f (x) = 2 x - 00 (vi) x = 0 is a vertical asymptote (vii) f(1) = 3