The temperature at a point (x, y, z) is given by T(x, y, z) = 200e-x² - 3y² - 72² where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature (in °C/m) at the point P(4, -1, 2) in the direction toward the point (5, -5, 5). °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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