Suppose that a function z = f ( x , y ) {\displaystyle \displaystyle z=f(x,y)} is implicitly defined by an equation: x y z + x + y 2 + z 3 = 0 {\displaystyle \displaystyle xyz+x+y^{2}+z^{3}=0}
(b) If f ( − 1 , 1 ) < 0 {\displaystyle \displaystyle f(-1,1)<0} , find the linear approximation of the function z = f ( x , y ) {\displaystyle \displaystyle z=f(x,y)} at ( − 1 , 1 ) {\displaystyle \displaystyle (-1,1)} .
