This question was especially difficult for myself and I stressed for literally two days and nights on it. I've been working on this assignment for literally the entire week but these last few questions have me utterly stumped

Chiara, David and Sameer decide to go on a hike on a mountain whose altitude is given by the function H($,y) =100 3:2 y2 +$y and they meet at the point of coordinates x = 4 and y = 5. 5.a I [6 points] They rst decide to warm up a little, so from their meeting point, they want to walk in such a way that their altitude does not change. Give a direction in which they should start walking. Your answer should be a unit vector. After a couple of rounds on their path with constant altitude, which they call 79, they decide to separate. The following questions are all independent from each other! 5.b I [4 points] Chiara goes to the point with coordinates (5.1, 2.02) and she buries in the ground a piece of paper with an approximation of the altitude at that point that she computed using linearization. What number did Chiara write on the paper? 5.c I [4 points] David goes back to the initial point (4, 5) and decides to follow a linear path towards the point with coordinates (3, 6). What is the rate of change of David's altitude at the beginning of his solitary hike? 5.d I [10 points] Sameer, instead, feels ready to climb the mountain and decides to start his climb at one of the points, along the path 'P, where the mountain is the steepest. What are the coordinates of one of these points? You can assume that a polm' with that property exists