Maximum value on a circle I need to find the maximum value of a function on a circle: Let $C$ denote the circle of radius $6$ centered at the origin in the $xy$-plane. Find the maximum value of $x^2y$ on $C$. Where do I even start with this?

Hint: For $(x,y)$ on the circle of radius $6$, we have 
$$
x^2=36-y^2
$$
So you can find a single variable function to maximize.
