I am Calculus AB student. I know how to find first derivative, second derivative, prove points of inflecition, find concavity...but as I just finnished the last section of chapter 4 and chapter 5 is Integrals, I still have one question that remains unanswered: Why is it important to find concavity? I know that f"(x) lets you find accelelration fro distance, and Jerk from speed, but why do I care that a function is concave up from (-inf, -2) Reunited with (4, inf) ? is it going to make any application that will be needed for? Everything I studied so far made mo reference to concavity. Critical points that give the mins and maxes in first derivative...those are useful. but my question stays: What is concavity and Inflection points important for?