Concave describes an inward curve; its opposite, convex, describes a curve that bulges outward. They are used to describe gentle, subtle curves, like the kinds found in mirrors or lenses.
A graph is said to be concave up at a point if the tangent line to the graph at that point lies below the graph in the vicinity of the point and concave down at a point if the tangent line lies above the graph in the vicinity of the point.
A point where the concavity changes (from up to down or down to up) is called a point of inflection (POI).
A graph is said to be concave up at a point if the tangent line to the graph at that point lies below the graph in the vicinity of the point and concave down at a point if the tangent line lies above the graph in the vicinity of the point.
A point where the concavity changes (from up to down or down to up) is called a point of inflection (POI).