Provide an Appropriate Response $(a, b)$ On the Surface Of $z=f(x, y)$

Multiple Choice

Provide an appropriate response.
-If we are looking for the critical points $(a, b)$ on the surface of $z=f(x, y)$ , then we study the tangent lines to $(a, b)$ along the slices parallel to the $x$ -axis and $y$ -axis. These tangent lines must have which of the following properties?
(i) They must be perpendicular.
(ii) They must be horizontal.
(iii) They must be horizontal, but not perpendicular.
(iv) They must be perpendicular, but not horizontal.

A) Both (i) and (ii) are correct.
B) Only (ii) is correct.
C) Only (iii) is correct.
D) Only (iv) is correct.