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The temperature at a point (x, y, z) is given by T(x, y, z) = 100e^(−x^2...

The temperature at a point (x, y, z) is given by T(x, y, z) = 100e^(−x^2 − 3y^2 − 9z^2) 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 (5, −2, 3). (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.

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