Find the point(s) at which f achieves a local maximum.
Find the point(s) at which f achieves a local minimum.
Find the intervals on which f is concave up.
Find the intervals on which f is concave down.
Find all inflection points.
we must find f' and f'' f'=6x^2-24 f'=0 x=-2, x=2 f"=12x^2 f"=0 x=0 increase where f'>0 so at x from(-infinity, -2) and(2, +infinity) decrease where f'<0 so x from (-2 , 2) local maximum x=-2 local minimum x=2 concave up where f"<0 concave down where f">0 12x^2>0 if x not zerox=0 is not inflection point because function does notchange type of concavity at x=0