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6. (5 marks) Consider the function f defined by f (x, y) = ln(x − y)....

6. Consider the function f defined by f (x, y) = ln(x − y). (a) Determine the natural domain of f. (b) Sketch the level curves of f for the values k = −2, 0, 2. (c) Find the gradient of f at the point (2,1), that is ∇f(2,1). (d) In which unit vector direction, at the point (2,1), is the directional derivative of f the smallest and what is the directional derivative in that direction?

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