Hypograph (mathematics) in the context of Concave function

In mathematics, a concave function is one for which the function value at any convex combination of elements in the domain is greater than or equal to that convex combination of those domain elements. Equivalently, a concave function is any function for which the hypograph is convex. The class of concave functions is in a sense the opposite of the class of convex functions. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap, or upper convex.