A function of a single variable is concave if every line segment joining two points on its graph does not lie above the graph at any point. Symmetrically, a function of a single variable is convex if every line segment joining two points on its graph does not lie below the graph at any point.

How do you know if a function is concave or convex?

To find out if it is concave or convex, look at the second derivative. If the result is positive, it is convex. If it is negative, then it is concave.

How do you know if a function is concave?

To find when a function is concave, you must first take the 2nd derivative, then set it equal to 0, and then find between which zero values the function is negative. Now test values on all sides of these to find when the function is negative, and therefore decreasing.