The temperature T at point (x, y) on a metal plate is given by: T(x, y)...

 

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The temperature T at point (x, y) on a metal plate is given by: T(x, y) = ye-x-9y2 a. Find the rate of change of temperature at the point P(-3,1) toward the point Q(2,5). (3 marks) b. In which direction does the temperature increase fastest at P? Express your answer as both a unit vector and an angle relative to the positive x-axis, in radians. (2 marks) c. What is the maximum rate of change of temperature at point P? (1 mark) Find the absolute maximum and minimum values of the following function f on the given set D. f(x,y) = xyx + 8y D= {(x,y) = R | -2 y 9-x2} The temperature T at point (x, y) on a metal plate is given by: T(x, y) = ye-x-9y2 a. Find the rate of change of temperature at the point P(-3,1) toward the point Q(2,5). (3 marks) b. In which direction does the temperature increase fastest at P? Express your answer as both a unit vector and an angle relative to the positive x-axis, in radians. (2 marks) c. What is the maximum rate of change of temperature at point P? (1 mark) Find the absolute maximum and minimum values of the following function f on the given set D. f(x,y) = xyx + 8y D= {(x,y) = R | -2 y 9-x2}