The temperature at a point (x, y, z} is given by 2 2 2 T(X, y, z} = 4DDe'X _ 3V _ 72 where T is measured in C and X, y, z in meters. (a) Find the rate of change of temperature (in c'C,'m) at the point P(4, 1, 5) in the direction toward the point {5, 4, 6). (6688}e144 ocxm X (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P. 6688[e_144)