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:
Remark: A saddle point is a stationary point that is not a minimum or 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: A saddle point is a stationary point that is not a minimum or a maximum location of the function.