Suppose that
$ f(x,y,z) = \frac{3}{2-x} + \frac{1}{y-z} $
and let $S$ be the surface given by the equation
$f(x,y,z) = 1$
Are there any points on $S$ where the tangent plane to $S$ is parallel to the $xy$, $xz$ or $yz$–planes? If such points exist find them. If no such points exist, explain why.
Do we find the gradient vectors of both $S$ and the plane we are checking.
And find the values of $x,y,x$ such that one gradient vector is a scalar multiple of the other?
Would this be how we approach the question?
