Determine where f is increasing and where f is decreasing

Question

Problem - f(x) = (x³ - 1/x³ + 1).

a) Find the domain of f(x), the intercept of f(x), and any symmetry of f(x).

b) Determine where f is increasing and where f is decreasing.

c) Find all local maxima and minima of f.

d) Determine where f is concave up and where f is concave down.

e) Find all inflection points of f.

f) Determine the vertical and horizontal asymptotes of f, if any. Justify your answer.

g) Sketch the graph of f, clearly indicating all of the information obtained above.