The temperature at a point (x, y, z) is given by T(x, y, z) = 100e-x2 - 5y2 - 722 where T is measured in .C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(2, -1, 2) in the direction towards the point (3, -4, 5). .C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P