DefinitionConcavity is a a property but of functions, not of numbers is concavity, it is a geometric property of the graph. When the graph exceeds the tangent lines at every point, the function is said to be concave upward, and when the graph is below the tangent lines, it is concave downwards. Inflection points are points on graph where the concavity changes, telling us when the direction of curvature changes. In calculus and optimization, concavity is a mean by which we can categorize the nature of certain behavior of functions and the location of certain critical points, known as inflection points. For example, the function f(x)=x3 is concave up for x>0; concave down for x<0. At (0,0): This is an inflection point; the concavity changes from up to down.
