How do I learn how to sketch the admissible points of functions, such as $$max\space f(x,y)=xy$$ with constraints $$4x^{2}+9y^{2}\leq36$$ $$2x+3y\geq6$$
and $$min \space f(x,y)=xy^{2}+5x^{3}y-xy$$ For linear functions, it is pretty straight forward where we set $x$ and $y$ for some numbers set up in a table, and then we can draw from that. But how do we do it for functions where the variables are multiplied with each other?
Thanks