# Concave Function

In mathematics, concave function and convex function play an important role. Both the functions are related to each other. A concave function is the negative of a convex function. A function $f(x)$ is concave over a convex set if the function: $f(x)$ is a convex function over the set. Then, the result obtained for convex functions can be modified into result for concave functions by multiplication by -1 and vice versa. A concave function is also called as concave downwards, convex upwards, concave down, upper convex or convex cap.

The negative of a convex function is a concave function. Also sum of the concave functions is a concave function.