In mathematics, a concave function is the negative of a convex function. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap, or upper convex.
A real-valued function on an interval (or, more generally, a convex set in vector space) is said to be concave if, for any and in the interval and for any ,
A function is called strictly concave if
for any and .
For a function , this second definition merely states that for every strictly between and , the point on the graph of is above the straight line joining the points and .
A function is quasiconcave if the upper contour sets of the function are convex sets.