Sumários

2 Maio 2024, 13:00 • Annabela Pelicano

Teorema de Weierstrass.

Método dos intervalos fechados.

Resolução de exercícios.

2 Maio 2024, 11:00 • Pedro Alexandre Correia de Matos

- Introduction to Optimization of 2-variable functions: unconstrained extrema

Definition of maximum point, local minimum point, local maximal value and local minimal value of a 2-variable function. Examples;
Definition of absolute maximum point and absolute minimum point of a 2-variable function. Extreme values of a 2-variable function: definition of absolute maximum value and absolute minimum value. Examples;
Critical points of a 2-variable function. Characterization of local maximum points and local minimum points as critical points (Fermat's theorem);
Saddle points of a 2-variable function. Examples;
Qualitative description of local maximum points, local minimum points and saddle points using contour maps;

Motivation: the proof of the second derivative test for 1-variable functions using quadratic approximation;
The quadratic approximation of a 2-variable function at a point where the second-order partial derivatives are continuous;

- CUP Week 10 - Ex. 2 (calculation of critical points and qualitative description of these), Ex. 7 (brief comment).

2 Maio 2024, 11:00 • Luca Scala

Extremos livres. Pontos criticos. Criterio da derivada segunda.

2 Maio 2024, 11:00 • Cristiana João Soares da Silva

Planos tangentes a superfícies de nível.

Retas normais a uma superfície de nível.

Exercícios 7 (terminar) e 8 da PUC (semana 9).

Otimização em R^n.

Máximos e mínimos locais. Definição, exemplos.