The 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(2, −1, 2) in the direction towards the point
(4, −4, 4). answer in °C/m
(b) In which direction does the temperature increase fastest at
P?
(c) Find the maximum rate of increase at P.