# Thread: Finding All Critical Points of f(x,y)

1. ## Finding All Critical Points of f(x,y)

I'm having some trouble finding all the critical points of the following function.

See figure attached for function and my work.

How can I get the equation of the line that contains all those critical points?

Thanks again!

2. the first and second lines of your solution should be:

$f_{x} = 3x^2y^3 - 2xy^2 = xy^2(3xy-2)$

and $f_{y}=3x^3y^2-2x^2y=x^2y(3xy-2)$