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f(x) = x^3 2x + 1/x A - Find any horizontal asymptotes of f. B - Find any vertical asymptotes of f. C - Find the intervals on which f is...

f(x) = x^3 − 2x + 1/x

A - Find any horizontal asymptotes of f.

B - Find any vertical asymptotes of f.

C - Find the intervals on which f is increasing/decreasing.

D - Find any local maxima or minima of f. Give the point on the graph, not just the x-coordinate

E - Find the intervals on which f is concave up/down.

F - Find any inflection points of f. Give the point on the graph, not just the x-coordinate.

G -  Sketch the graph of f. Make sure your drawing is consistent with the information above, and any solutions to f(x) = 0.

H -  Does f have an absolute maximum (on the entire real line)?

I -  Does f have an absolute minimum (on the entire real line)?

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