The temperature at a point (x,y,z) is given by \(\displaystyle
T(x,y,z) = 200e^{-x^2 -y^2/4 - z^2/9}\text{,}\) 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 (3, -3, 5).

In which direction (unit vector) does the temperature increase the fastest at (-1, 1, 1)?

\(\langle\), ,\(\rangle\)

What is the maximum rate of increase of \(T\) at (-1, 1, 1)?