The temperature at a point (x, y, z) is given by -x² - sy² - 722 T(x, y, z) = 100e 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(2, -1, 4) in the direction toward the point (5, -4, 5). 7400 -121 e °C/m V 19 (b) In which direction does the temperature increase fastest at P? -400e-121 1,200e -121 - 5600e 121 (c) Find the maximum rate of increase at P. 100/3156 e -121

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A:

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A: