2. (6 points) You are at the point p = (1,0, arctan(2)) on a hill with elevation function H(x, y) = arctan(2x + y). The positive x-axis indicates east, and the positive y-direction indicates north. (a) Sketch some level curves of H. In your sketch, indicate (1,0) and draw VH(1,0). (b) Starting from p, in what direction should you walk in order to descend the hill the fastest? Express your answer as a unit vector. (c) Suppose you walk southeast from p. (i) Are you initially ascending the hill, or de- scending the hill? (ii) Is the hill initially getting steeper, or getting flatter? Briefly explain. 2. (6 points) You are at the point p = (1,0, arctan(2)) on a hill with elevation function H(x, y) = arctan(2x + y). The positive x-axis indicates east, and the positive y-direction indicates north. (a) Sketch some level curves of H. In your sketch, indicate (1,0) and draw VH(1,0). (b) Starting from p, in what direction should you walk in order to descend the hill the fastest? Express your answer as a unit vector. (c) Suppose you walk southeast from p. (i) Are you initially ascending the hill, or de- scending the hill? (ii) Is the hill initially getting steeper, or getting flatter? Briefly explain