Question: The temperature at a point ( x , y , z ) is given by T ( x , y , z ) = 300

The temperature at a point (x, y, z) is given by

T(x, y, z) = 300ex2 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(4, 1, 2) in the direction towards the point (6, 3, 6).

C/m

(b) In which direction does the temperature increase fastest at P?

(c) Find the maximum rate of increase at P.

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