Question

Or f(x, y), find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = 1 x + 1 y + xy

Answer 1

$f(x,y)=x+y+xy$
$f_x=1+y=0\implies y=-1$
$f_y=1+x=0\implies x=-1$