I am having difficulty understanding what this question is asking for, and was wondering if someone could shed some light on it.
$f: \mathbb R^{m} \rightarrow \mathbb R$ is defined by
$f(x, y, z)=z^{2} - x^{2} - y^{2}$
Define the level set of $f$ for the value c to be
$\sum_{c} := \{x \in \mathbb R : f(x) = c \}$
Compute $\nabla f$. Indicate $\nabla f$ as a vector at the points $(1,0,0), (0,1,0),(0,0,1)$ on the corresponding level sets.
I know that $\nabla f(x,y,z) = (-2x, -2y, 2z)$. Is the question asking for the value of $\nabla f$ at the points $(1,0,0), (0,1,0),(0,0,1)$ or does it want to be expressed in terms of these points, or something else entirely?