Provide an Appropriate Response $f(x, y)$ , Which of the Following Statements Is True?
(I)

Provide an appropriate response.
-Given $f(x, y)$ , which of the following statements is true?
(i) $f_{X}$ is the rate of change of $f$ as $x$ and $y$ change.
(ii) $f_{X}$ is the rate of change of $f$ as $x$ changes, but $y$ stays fixed.
(iii) $f_{y}$ is the rate of change of $f$ as $y$ changes, but $x$ stays fixed.
(iv) $f_{X}$ is the rate of change of $f$ as $f$ changes, but $x$ stays fixed.

A) Only (iii) is correct.
B) (iv) could be correct under certain conditions.
C) Both (ii) and (iii) are correct.
D) Only (i) is correct.