The temperature at a point $(x,y,z)$ is given by $$T(x,y,z) = 1100 e^{-x^2-2y^2-z^2}$$ where $T$ is measured in $^{\circ}\text{C}$ and $x$, $y$, and $z$ in meters.

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1. Find the rate of change of the temperature at the point $P(2,-2,2)$ in the direction toward the point $Q(3,-4,3).$
Answer: $D_{\overrightarrow{PQ}}\,f(2,-2,2) =$

2. In what direction does the temperature increase fastest at $P$?
Answer:

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

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