We are given the function:
$$f(x,y)=x^2+xy+x+y^2$$
On the set $S=\{(x,y):x^2+y^2 \leq 9\}$
I found the critical point on the interior of $S$ to be $(-2/3,1/3)$.
I am asked to parametrize the boundary of $S$ in terms of theta using sine and cosine, and write $f$ in terms of theta on the boundary. (don't forget restrictions on theta).
I'm not sure how to do this.
After we do that, we are asked to find the extrema of $f$ on $S$. I am also not sure how to do this.
Any help would be immensely appreciated!