Q8Single correct5 Marks21 Dec 2025

Let $f: \mathbb{R}^2 \to \mathbb{R}$ be a function. Consider the following statements. S1: The partial derivatives of $f$ exist and are continuous at all points. S2: The function $f$ is continuous. Which of the following is true?

A

Neither of the two statements implies the other.

B

S1 holds if and only if S2 holds.

C

S1 implies S2, but S2 does not imply S1.

D

S2 implies S1, but S1 does not imply S2.