Problem 11.1: You know that $d/dt f(\vec{r}(t)) = 19$ at $t = 7$ if $\vec{r}(t) = [t, t]$ \\
and $d/dt f(\vec{r}(t)) = 11$ at $t = 7$. $\vec{r}(t) = [t, 14 - t]$. Find the gradient of $f$ at \\
$(7, 7)$. \\
Problem 11.2: The pressure in the space at the position $(x, y, z)$ is \\
p$(x, y, z) = x^2 + y^2 - z^3$ and the trajectory of an observer is the curve \\
$\vec{r}(t) = [t, t, 1/t]$. Using the chain rule, compute the rate of change of the \\
pressure the observer measures at time $t = 2$.
