- #1

der.physika

- 38

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[tex]f(x,y)=xy^2[/tex] with domain [tex]x^2+y^2\leq4[/tex]

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.

[tex]f_x=y^2=0[/tex] [tex]f_y=2yx=0[/tex]

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 [tex](x,y)=(0,0)[/tex]

Plug into the matrix [tex]\left(\begin{array}{cc}f_x_x&f_x_y\\f_x_y&f_y_y\end{array}\right)[/tex]

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

Plug into the matrix [tex]\left(\begin{array}{cc}f_x_x&f_x_y\\f_x_y&f_y_y\end{array}\right)[/tex]

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