Question: The temperature at a point (x, y, z) is given by T ( x , y , z ) = 200 e x 2 3

The temperature at a point (x, y, z) is given by T(x,y,z)=200ex23y29z2 where T is measured in Celsius and x, y, and z in meters.

  1. Find the rate of change of temperature at the point P(2, 1, 2) in the direction u = (1, 2, 1).
  2. In which direction does the temperature increase fastest at P?
  3. Find the maximum rate of increase at P.

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