**Concavity** is a geometric term which describes a curve. In calculus, a graph is **concave upward** if the derivative, *f* '(*x*) (of the function, *f*(*x*) being graphed) is increasing upon an interval; a graph is **concave downward** if the derivative is decreasing. In other words, if the second derivative, *f* ''(*x*), is positive (or, if the acceleration is positive); then, the graph is concave upward; if the second derivative is negative; then, the graph is concave downward. Points where concavity changes are inflection pointss.

The "bottom" of a concave downward slope will have a point known as the minimal extremum; the "apex" of a concave upward slope will have a point known as the maximal extremum.

In mathematics, a function is said to be **concave** on an interval if, for all *x*,*y* in .

If is differentiable, then is concave iff is monotone decreasing.

If is twice-differentiable, then is concave iff is negative.

See also: convex