1
$T(x, y, z) = \frac{1}{x^2 + y^2 + z^2}$
be the temperature at the position $(x, y, z) \neq (0, 0, 0)$ in the 3-space. (We are not going to care about units.)
At the position $(1, 2, 3)$, find a vector that indicates the direction to which the temperature changes the
fastest.