3. (8 marks) Contour lines for a function /(x, y) are drawn in the diagram below. They are spaced at intervals of z = 1 and the contours from z = -4 to z = 4 are marked. The action for much of this problem is at x = -1, y = 1. It's useful to draw these two lines. The x-axis is horizontal and the y-axis is vertical. (a) Draw a rough graph of f(x, 1) on the interval [-2, 2]. Try to get the concavity of the graph right. (b) Draw a rough graph of /(-1, y) on the interval [-2, 2]. (c) Draw a rough graph of f(x, 0) on the interval [-4, 4]. (d) Provide an estimate of the partial derivatives /, and /, at the point (-1, 1). (e) Provide the sign (pos or neg) of the second partial derivatives, fox, fyyand fry at the point (-1, 1). Give clear convincing arguments to justify your answer. (f) Find the equation of the tangent plane to the graph z = /(x. y) at the point (-1, 1). Write it in the form: z = a(x + 1) + b(y - 1) +c