Let $f(w,x,y,z) = wz - xy$. Choose the correct statement(s) from below:\\
(A) The directional derivative at $(1,0,0,1)$ in the direction $(a,b,c,d)$ is 0 if $a + d = 0$;\\
(B) The directional derivative at $(1,0,0,1)$ in the direction $(a,b,c,d)$ is 0 only if $a + d = 0$;\\
(C) The vector $(0,-1,-1,0)$ is normal to $f^{-1}(1)$ at the point $(1,0,0,1)$;\\
(D) The set of points $(a,b,c,d)$ where the total derivative of $f$ is zero is finite.