# Concave function

## Negative of a convex function / From Wikipedia, the free encyclopedia

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In mathematics, a **concave function** is one for which the value at any convex combination of elements in the domain is greater than or equal to the convex combination of the values at the endpoints. 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**.