Question 1 Define a function by (a) (b) (c) f(x, y) = ex+xy-3x State the domain...

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Question 1 Define a function by (a) (b) (c) f(x, y) = ex+xy-3x State the domain and range of the f(x,y). Evaluate an equation that describes its level set and sketch it for f(x,y) = e using a graph plotter. (5 marks) Calculate the gradient vector of f(x,y) at the point (1, -1) and hence state a direction where f(x,y) does not change at this point. (7 marks) Determine the rate of change of f(x,y) at point (1, -1) in the direction of u = 3i - j. Does the function increase or decrease in this direction? (5 marks) (a) Determine all critical points of f(x,y) and apply the 2nd derivative test to classify them. (18 marks) Question 1 Define a function by (a) (b) (c) f(x, y) = ex+xy-3x State the domain and range of the f(x,y). Evaluate an equation that describes its level set and sketch it for f(x,y) = e using a graph plotter. (5 marks) Calculate the gradient vector of f(x,y) at the point (1, -1) and hence state a direction where f(x,y) does not change at this point. (7 marks) Determine the rate of change of f(x,y) at point (1, -1) in the direction of u = 3i - j. Does the function increase or decrease in this direction? (5 marks) (a) Determine all critical points of f(x,y) and apply the 2nd derivative test to classify them. (18 marks)