Let the temperature distribution on a flat plate in degrees F be given by f(x, y),...

 

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Let the temperature distribution on a flat plate in degrees F be given by f(x, y), where (x,y) are the coordinates of a typical point on the plate, measured in feet. Consider the points P(1, 1), Q(2,3) and R(-3,3). At the point P let the rate of change of change of temperature in the direction of the vector PQ be √5 °F per foot and in the direction of the vector PR be -2/√5°F per foot. (a) Find the direction in which the temperature decreases most rapidly at P, and find the magnitude of this rate of decrease. (b) If f(1, 1) = 20°F, then find the linear approximation to f(x, y) at P. Let the temperature distribution on a flat plate in degrees F be given by f(x, y), where (x,y) are the coordinates of a typical point on the plate, measured in feet. Consider the points P(1, 1), Q(2,3) and R(-3,3). At the point P let the rate of change of change of temperature in the direction of the vector PQ be √5 °F per foot and in the direction of the vector PR be -2/√5°F per foot. (a) Find the direction in which the temperature decreases most rapidly at P, and find the magnitude of this rate of decrease. (b) If f(1, 1) = 20°F, then find the linear approximation to f(x, y) at P.

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ANSWER a To find the direction in which the temperature decreases most rapidly at point P we need to ... View the full answer