He temperature at a point (x, y, z) is given by T(x, y, z) = 100e−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, 4) in the direction towards the point (6, −4, 5). °C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.