The temperature at a point

(x, y, z)

is given by

t(x, y, z) = 300e−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, 3)

in the direction towards the point

(5, −3, 4).

°c/m

(b) in which direction does the temperature increase fastest at p?

(c) find the maximum rate of increase at p.

expert answer