## Function optimization

### Teaching unit

### Description

Optimización de funciones de una y varias variables.

### Objectives

Acquire and use mathematical language fluently, both orally and in writing, and rigorous formalization and structuring of a real problem in the form of mathematical problem.

Ability to apply knowledge, methods and algorithms to situations and problems in the area of economic enterprise.

Correctly handle the literature and information sources available to strengthen and expand knowledge and increase torque capacity to pose and solve mathematical so many problems that may arise and relate to the subject.

Use various technological tools (such as computer software) that facilitate solving math problems and understand the limitations of such tools.

Knowledge and skill in handling major real functions of real variable linear, quadratic, polynomial, rational, trigonometric, exponential, logarithmic. Being able to use them as a tool to solve a large variety of problems.

Correctly interpret graphic representations of functions and their level curves.

Understand the concept of derivative of a function and its economic interpretation.

Calculate derivatives of functions of several variables, both first order and higher orders. Use them to solve optimization problems.

### Subjects

#### Lecture topics

- Closed, bounded and compact sets.
- Relative and absolute extremes of functions of one variable. Turning points
- Relative and absolute extremes of functions of several variables.
- Absolute extremes on compact sets.
- Conditioned extremes

#### Laboratory topics

- Calculus of maximum and minimum of functions of several variables.
- Calculation of conditioned extremes.