(a) Show that the surface f(x,y)= 2x -6.xy + 3y has two critical points [6 marks]...

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(a) Show that the surface f(x,y)= 2x -6.xy + 3y has two critical points [6 marks] – a saddle point at (0,0,0) and a local minimum at (1,1.-1) [9 marks]. (15 marks) (b) Let f(x, y) = In(x* + y'). Find the two partial derivatives af /Əx and o flax by suitable means [6 marks], and hence show that the function f(x, y) satisfies Laplace's Equation [4 marks] af ôf =0. (10 marks) (a) Show that the surface f(x,y)= 2x -6.xy + 3y has two critical points [6 marks] – a saddle point at (0,0,0) and a local minimum at (1,1.-1) [9 marks]. (15 marks) (b) Let f(x, y) = In(x* + y'). Find the two partial derivatives af /Əx and o flax by suitable means [6 marks], and hence show that the function f(x, y) satisfies Laplace's Equation [4 marks] af ôf =0. (10 marks)