**Introduction:**If a convex function has a stationary point, then we can immediately conclude that this stationary point is a minimum location of the function. Similarly, it follows that a stationary point of a concave function is a maximum location of the function.

**Theorem:**

- A convex function has a minimum in a stationary point.
- A concave function has a maximum in a stationary point.

**Remark:**Also when a function is convex on part of the domain the stationary points in this parts are minimum locations of the function. The stationary points on the other parts of the domain are then maximum locations.