Suppose that the temperature at a point (x, y, z) in space is given by:
T(x, y, z) = 80/(1 + x^2 + 2y^2 + 3z^2), where T is measured in degrees Celsius and x, y, z in meters.
In which direction(find a unit vector) does the temperature T increase fastest at the point (1, 1, - 2)? What is the maximum rate of increase?