# Absolute Max/Min

Can anyone tell me the general procedure in doing the following procedure?

$$f(x,y)=xy^2$$ with domain $$x^2+y^2\leq4$$

Find it's absolute max & absolute min.

Okay, here is my thought procedure, tell me what I can fix.

So I would basically say, find the partial derivatives with respect to x and y and set them equal to zero.

$$f_x=y^2=0$$ $$f_y=2yx=0$$

so what's up? I plug that into the original equation? and then do the whole matrix thing to find if it's an absolute max or min? so point $$(x,y)=(0,0)$$

Plug into the matrix $$\left(\begin{array}{cc}f_x_x&f_x_y\\f_x_y&f_y_y\end{array}\right)$$

But I don't know how I would go about considering the $$x^2+y^2\leq4$$, do I find the boundary point? What are those? $$(x,y)=(2,0)=(0,2)=(-2,0)=(0,-2)$$ and then plug it into the original equation and then use

Plug into the matrix $$\left(\begin{array}{cc}f_x_x&f_x_y\\f_x_y&f_y_y\end{array}\right)$$

Am I on the right track? Can someone show me some guidance?