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The temperature at a point (x, y, z) is given by T(x, y, z) = 400e−x2...

The temperature at a point (x, y, z) is given by T(x, y, z) = 400e−x2 − 5y2 − 9z2 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 (3, −5, 6). °C/m

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

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

Math   Calculus   
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