Let f(x, y), g(x, y) be differentiable functions, and let k be a real number. Consider f constrained on the domain g(x, y) k, y k (a) (b) Assume the system of equalities g(x, y) = k and Vf = g(x, y) has a solution (2, 4, 1) = (10,4,3). Explain the significance of this point when optimizing the function f on the constrained domain. Assume the system of equalities g(x, y) = k and Vf = \Vg(,y) has a solution (x, y, 1) = 0,-1,2). A point (xo, yo) on the oval-shaped portion of the constrained domain must satisfy this system of inequalities with a negative Lagrange Multiplier. Through any combination of pictures and/or words, provide an intuitive argument to justify this fact. Based on the shape of constrained domain that is graphed, it appears each of the points (-4, 2) and (6,2) must satisfy complementary slackness. Through any combination of pictures and/or words, provide an intuitive argument to justify this fact. (c) Let f(x, y), g(x, y) be differentiable functions, and let k be a real number. Consider f constrained on the domain g(x, y) k, y k (a) (b) Assume the system of equalities g(x, y) = k and Vf = g(x, y) has a solution (2, 4, 1) = (10,4,3). Explain the significance of this point when optimizing the function f on the constrained domain. Assume the system of equalities g(x, y) = k and Vf = \Vg(,y) has a solution (x, y, 1) = 0,-1,2). A point (xo, yo) on the oval-shaped portion of the constrained domain must satisfy this system of inequalities with a negative Lagrange Multiplier. Through any combination of pictures and/or words, provide an intuitive argument to justify this fact. Based on the shape of constrained domain that is graphed, it appears each of the points (-4, 2) and (6,2) must satisfy complementary slackness. Through any combination of pictures and/or words, provide an intuitive argument to justify this fact. (c)