Why is Concavity and Inflection Points Important for Calculus AB?

[Robokapp]

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) let's 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?

 

[Integral]

After you find the mins and maxs with the first derivative, you use the 2nd derivative (concavity) to determine if a point is a max or a min. Concave up implies a max, concave down implies a min.

 

[Robokapp]

After you find the mins and maxs with the first derivative, you use the 2nd derivative (concavity) to determine if a point is a max or a min. Concave up implies a max, concave down implies a min.

Don't you do that by looking at the sign changes in f'(x) and if it comes from - to + it's a min, and from + to - it's a max? That's how I learned it.