Q10Multiple correct2 Marks31 Aug 2025

Let $f: \mathbb{R}^2 \to \mathbb{R}$ be a function. Choose all the true statements from the options below if it is known that the function is differentiable at a point $(c, c)$ in $\mathbb{R}^2$.

A

f is continuous at $(c, c)$.

B

The hyperplane to the graph of f exists at $(c, c)$.

C

The Hessian matrix of f exists at $(c, c)$.

D

The gradient of f exists at $(c, c)$.