This is looking at how the CURVE of the graph opens–concave up (positive parabola) or concave down (negative parabola).
Definition: If a function’s graph is BELOW all of its tangent line, concave down. If a function’s graph is ABOVE all of its tangent line, concave up– hence why we use the 2nd derivative to determine concavity from the 1st derivative (tangent line).
The inflection point is where the function switched from concave down->up or vice versa. Do not get this confused with the critical points as we use the f”(x) for the inflection points.
Second Derivative Test (cr: Organic Chemistry Tutor)
Concavity, Inflection Points, and Second Derivative (cr: The Organic Chemistry Tutor)