Concavity refers to the curvature of a graph or a function. A function is considered concave up if it curves upwards, resembling a cup that can hold water. This means that the slope of the function is increasing. Conversely, a function is concave down if it curves downwards, like an upside-down cup, indicating that the slope is decreasing. In mathematics, concavity is important for understanding the behavior of functions and their critical points. The second derivative test is often used to determine concavity. If the second derivative is positive, the function is concave up; if negative, it is concave down.