Concavity is a geometric term which describes a curve. In calculus, a graph is concave upward if the derivative, f '(x) (of the function, f(x) being graphed) is increasing upon an interval; a graph is concave downward if the derivative is decreasing. In other words, if the second derivative, f ''(x), is positive (or, if the acceleration is positive); then, the graph is concave upward; if the second derivative is negative; then, the graph is concave downward. Points where concavity changes are inflection pointss.
See also: convex