Question 3 The temperature in C over a flat surface is described by the function T(x,...

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Question 3 The temperature in C over a flat surface is described by the function T(x, y) = xy+ 2x + y. (a) Determine all local stationary points of the temperature function and classify them. Calculate the temperatures at these points. (15 marks) (b) O Over the semi-circular region x + y 16, y 0, determine the lowest and highest temperatures attained and their locations. State any theorem used. (15 marks) If the region in part (b) is expanded to the disc x + y 16, without calculations, explain if and how your answers in part (b) would change. You may use a graph plotter to aid your explanations. (5 marks) Question 3 The temperature in C over a flat surface is described by the function T(x, y) = xy+ 2x + y. (a) Determine all local stationary points of the temperature function and classify them. Calculate the temperatures at these points. (15 marks) (b) O Over the semi-circular region x + y 16, y 0, determine the lowest and highest temperatures attained and their locations. State any theorem used. (15 marks) If the region in part (b) is expanded to the disc x + y 16, without calculations, explain if and how your answers in part (b) would change. You may use a graph plotter to aid your explanations. (5 marks)