A real function is called convex or concave upward when the slope increases. Similarly, a function is called concave or concave downward when the slope decreases.
One way to test whether a function is convex or concave is to take the second derivative. If the second derivative over an interval is
- always positive, then the slope continually increases, and the function is convex
- always negative, then the slope continually decrease, and the function is concave