The temperature at a point (x, y, z) is given by

T(x, y, z) = 200e^-x2-3y2-9z2

where T is measured in 8C and x, y, z in meters.
(a) Find the rate of change of temperature at the point P(2, -1, 2) in the direction toward the point (3, -3, 3).
(b) In which direction does the temperature increase fastest at P?
(c) Find the maximum rate of increase at P.