The function f(x) =x³ +8/x² has derivatives f(x) =x³ -16/x³ and f"(x)=48/x⁴ (a) Determine the x- and y-intercepts. (b)

Question

The function f(x) =x³ +8/x² has derivatives f(x) =x³ -16/x³ and f"(x)=48/x⁴

(a) Determine the x- and y-intercepts.
(b) Determine the equations of any asymptotes and classify the
     behaviour at their endpoints.
(c) Determine the intervals of increase and decrease and classify any
     local extrema.
(d) Determine the intervals of concavity and identify any points of
      inflection.
(e) Complete the 2nd derivative test.
(f) Use this information to sketch the curve. Make sure all key features
    are clearly presented.

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