Provide a brief explanation or calculation to justify your answer: (a) Consider the contour plot for f(x,y) shown below. Use the contour plot to determine the sign y 13 please include all steps or i will give min 10 downvotes P 6 of each of the following derivatives of f at P. For each, write one sentence explaining your answer. (Assume the x and y axes have the same scale.) (i) f.(P) (ii) fy(P), (iii) Duf(P) where u = = (-2, -1) (iv) Duf(P) where u= (1,1). (b) The function f(x,y) = x++ + y2 and its partial derivatives are continuous in the region defined by >0 and y R. Calculate frutazy. (Note: 2+2 = x (x*), not (2")".) (c) Let g(x,y) be a function of x and y with the following data at different points (x, y). Suppose further that x and y are both functions of u and v with the following data at different points (u, v). Calculate og at the point (u, v) = (1,2). 9(1,2) 9(5,3) 9x(1,2) 9y(1.2) 9.(5,3) 9y(5,3) 2 -1 3 2 -2 4 (1.2) (1.2) (1.2) (5.3) *(5,3) 5 -2 - 1 -1 3 y(1.2) yu(1.2) yo(1.2) Yu(5,3) y(5,3) 3 2 0 1 3 Provide a brief explanation or calculation to justify your answer: (a) Consider the contour plot for f(x,y) shown below. Use the contour plot to determine the sign y 13 please include all steps or i will give min 10 downvotes P 6 of each of the following derivatives of f at P. For each, write one sentence explaining your answer. (Assume the x and y axes have the same scale.) (i) f.(P) (ii) fy(P), (iii) Duf(P) where u = = (-2, -1) (iv) Duf(P) where u= (1,1). (b) The function f(x,y) = x++ + y2 and its partial derivatives are continuous in the region defined by >0 and y R. Calculate frutazy. (Note: 2+2 = x (x*), not (2")".) (c) Let g(x,y) be a function of x and y with the following data at different points (x, y). Suppose further that x and y are both functions of u and v with the following data at different points (u, v). Calculate og at the point (u, v) = (1,2). 9(1,2) 9(5,3) 9x(1,2) 9y(1.2) 9.(5,3) 9y(5,3) 2 -1 3 2 -2 4 (1.2) (1.2) (1.2) (5.3) *(5,3) 5 -2 - 1 -1 3 y(1.2) yu(1.2) yo(1.2) Yu(5,3) y(5,3) 3 2 0 1 3