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?

If you have a circle of radius $6$ centered at the origin, then you know that every point on the circle satisfies $x^2+y^2=6^2$.
This lets you express your function in terms of one variable, which you can then take derivatives of to find the maxima.
Can you try from here?
