The temperature at a point (x, y, z) is given by t(x, y, z) = 100e−x2 − 5y2 − 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(2, −1, 3) in the direction towards the point (5, −4, 5). °c/m (b) in which direction does the temperature increase fastest at p? (c) find the maximum rate of increase at p.