The temperature at a point $(x,y,z)$ is given by

$T(x,y,z)=1400e^{-x^2-2y^2-z^2}$

where $T$ is measured in $C$ and $x,y,$ and $z$ in meters.

Find the rate of change of the temperature at the point $P(2,-3,2)$ in the direction toward the point $Q(3,-5,3).$

Answer: $D_{\text{v}\text{e}\text{c}(PQ)}f(2,-3,2)=$

In what direction does the temperature increase fastest at $P?$

Answer:

$3.$ Find the maximum rate of increase at $P.$

Answer: