(20 points) Sketch the graph of a single function /(2) which satisfies all of the following conditions. Label all local maxima and minima, intervals of increase and decrease, points of inflection, concavity, and asymptotes. (i) f(x) is defined for all real numbers 3(x2 - 3) (ii) f'(x) = - 2 (2:2 + 1 ) 12.n (ini) f" (x) = - (x:2 + 1)2 (iv) f(0) = 0 (v) /(3) = 3 () f(-3) ~ -3 (vii) lim f(x) = -co ( vili) lim /() = Do