Trying to find the critical points of $f(x,y) = y^2x - yx^2 + xy$.
I took partial derivative with respect to x, so
$F_x = y^2 - 2xy + y$
$F_x = y(y - 2x + 1)$
Then with respect to y,
$F_y = 2xy - x^2 + x$
$F_y = x( 2y - x + 1 )$
From here I don't know how to find critical points. I've tried solving for $x$ or $y$, but I end up having to cancel out variables which would destroy potential answers. I've also tried setting $F_x = 0$ but four answers gets expanded to 8 answers and I don't know how to go from there. I have a feeling I'm missing something obvious because this is one of the early questions from the book.