The temperature at a point (x, y, z) is given by T(x,y,z)=200ex23y29z2 where T is measured in Celsius and x, y, and z in meters.

1. Find the rate of change of temperature at the point P(2, 1, 2) in the direction u = (1, 2, 1).
2. In which direction does the temperature increase fastest at P?
3. Find the maximum rate of increase at P.