Q16Multiple correct3 Marks22 Dec 2024

Let f be a scalar-valued multivariable function defined on a domain D subset $\mathbb{R}^2$. Among the following statements, choose all the options which guarantee that the directional derivative of f exists in all directions, at a given point $(a, b)$ in D.

A

The gradient of f exists at $(a, b)$.

B

The function f is differentiable at $(a, b)$.

C

The gradient of f exists in a neighbourhood of $(a, b)$ and is continuous at $(a, b)$.

D

The partial derivatives of f exist at $(a, b)$.