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

T(x, y, z) = 300e^{x2 3y2 7z2}

where T is measured in C and x, y, z in meters.

(a) Find the rate of change of temperature at the point P(4, 1, 2) in the direction towards the point (6, 3, 6).

C/m

(b) In which direction does the temperature increase fastest at P?

(c) Find the maximum rate of increase at P.