The temperature at a point (x, y, z) is given by T(x, y, z) = 200e-x²-5y²-72² 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, 5) in the direction towards the point (5, -5, 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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