**Definition:**A function of two variables is convex on a part of the domain if the line segment between any two points of the graph of the function is above or on the graph of the function.

**Definition:**A function of two variables is concave on a part of the domain if the line segment between any two points of the graph of the function is below or on the graph of the function.

**Remark:**The definition of convexity and concavity for a function of two variables is basically not very different from the definition for a function of one variable.