Sumários

8 Maio 2024, 09:30 • Pedro Alexandre Correia de Matos

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

Motivation: existence of extreme values of continuous 1-variable functions defined in a closed interval and the possible occurrence of extreme values at the endpoints - the Closed Interval Method;
Interior points and boundary points of a subset of R^2. The interior and the boundary of a subset of R^2: examples;
Closed subsets of R^2: examples;
Bounded subsets of R^2: examples;
Existence of extreme values for continuous 2-variable functions defined in closed and bounded subset of R^2 - the Extreme Value Theorem (EVT);
The possible occurrence of extreme values at the boundary and boundary analysis: extension of the Closed Interval Method to continuous 2-variable functions defined in a closed an bounded subset of R^2;

- CUP Week 10 - Ex. 5 (item 36).