a) See the explanation below. b) See the explanation below. c) See the explanation below.
Work Step by Step
a) A closed set in $R^2$ is one that contains all of its boundary points. A bounded set is one that is contained within some disk (finite in extent). b) The extreme value theorem states the following. Suppose $f(x,y)$ is continuous on a closed and bounded set D in $R^2$. We can then state that $f$ attains absolute maximum values $f(x_1,y_1)$ and absolute minimum values $f(x_2,y_2)$ at some points in D. c) See section 9 of 14.7. i) Find the critical point of $f(x,y)$ in the domain $D$. ii) Find the extreme values of $f(x,y)$ in the domain $D$. iii) Compare i and ii for the largest (Absolute maximum) and smallest (absolute minimum) values.