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

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