The temperature at a point (x,y,z) is given by $\displaystyle T(x,y,z) = 200e^{-x^2 -y^2/4 - z^2/9}$, where $T$ is measured in degrees Celsius and x,y, and z in meters. There are lots of places to make silly errors in this problem; just try to keep track of what needs to be a unit vector.
Find the rate of change of the temperature at the point (-1, -1, 1) in the direction toward the point (5, -3, 2).


In which direction (unit vector) does the temperature increase the fastest at (-1, -1, 1)?
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What is the maximum rate of increase of $T$ at (-1, -1, 1)?