Answer
$f$ is increasing.
Work Step by Step
We have at $P$:
$\nabla {f_P} = \left( {2, - 4,4} \right)$ and ${\bf{v}} = \left( {2,1,3} \right)$
Using Theorem 2, the rate of change of $f$ is
$\frac{d}{{dt}}f\left( {{\bf{r}}\left( t \right)} \right) = \nabla T\left( {{\bf{r}}\left( t \right)} \right)\cdot{\bf{r}}'\left( t \right)$
$\frac{d}{{dt}}f\left( {{\bf{r}}\left( t \right)} \right) = \left( {2, - 4,4} \right)\cdot\left( {2,1,3} \right) = 12$
Since the rate of change is positive, $f$ is increasing.
