Determine where the graph of the given function is concave upward and concave downward. Find the coordinates of all inflection points.

g(t) = t² -27/t

Group of answer choices

upward for t < 0;="" downward="" for="" t="">0; no inflection

upward for t < 0="" and="" t=""> 3; downward for 0 < t="">< 3;="" inflection="" at="" (3,="" 0)="" and="" (0,="">

upward for t < 0="" and="" t=""> 3; downward for 0 < t="">< 3;="" inflection="" at="" (3,="">

upward for t > 3; downward for t < 3;="" inflection="" at="" (3,="">

please explain how you get to pick your answer thank you