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f(x) will be increasing where f '(x) is positive, and vice versa.
f(x) will be concave up where f '(x) has positive slopes, and vice versa.

Local max at x = −1; f'(x) changes from positive to negative.
Inflection points at x = −0.5, 0, 0.5; f '(x) changes slope.
Local min at x = 1; f '(x) changes from negative to positive.

See the hint in part (a).