Sumários
Lesson n. 28
3 Maio 2022, 11:00 • Rita Sousa
Maxima and Minima of functions of two variables.
Critical Points and Saddle Points. Second Derivatives Test.
Resolution of exercises: ex. 1 and 3, CUP-Week 10.
Lecture 28
3 Maio 2022, 09:30 • Rita Sousa
THEORY
- Definition of local maximum and local minimum of a two-variable function;
- Definition of critical point of a two-variable function;
- Definition of saddle point of a two-variable function;
- The quadratic approximation of a two-variable function at a point;
- The Hessian of a two-variable function at a point;
- The quadratic approximation of a function at a critical point, and the classification of this same point (as local maximum, local minimum or saddle point) using the Hessian of the function at the given point.
PRACTICE
The following exercises from CUP - Week 10 were discussed:
- Ex. 1 and 7
BIBLIOGRAPHY
Section 14.7 of J. Stewart, "Calculus - Early Transcendentals", 8th Edition, 2017, Cengage Learning.
Aula 28
3 Maio 2022, 08:00 • Rita Sousa
Extremos de funções de duas variáveis: definição de extremos, pontos críticos, teste das segundas derivadas. Revisão breve do caso de funções de uma variável e relação com o caso de duas variáveis. Exemplos.
Resolução de exercícios da semana 10 da PUC.