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The temperature at a point (x,y,z) is given by T(x,y,z)=200e−x2−y2/4−z2/9, where Tis measured in degrees celcius...

The temperature at a point (x,y,z) is given by T(x,y,z)=200e−x2−y2/4−z2/9, where Tis measured in degrees celcius 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 (0, 1, -2) in the direction toward the point (-1, -2, 5).

In which direction (unit vector) does the temperature increase the fastest at (0, 1, -2)?
〈 ,  , 〉 What is the maximum rate of increase of T at (0, 1, -2)?

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