The temperature at a point (x, y, z) is given by 400ex-3y2- 9z2 --_ (x, y, z) 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, 2) in the...

The temperature at a point

is given by

where
T
is measured in °C and

in meters.

Extracted text: The temperature at a point (x, y, z) is given by 400ex-3y2- 9z2 --_ (x, y, z) 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, 2) in the direction towards the point (5, -5, 6) oc/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.