100 70 1. (20 points) A hiker is climbing a mountain where the elevation of the mountain (in kilometers) is determined by the function f(x, y) = 2 - ( - ( 4 ) (a) What is the shape of the base of the mountain where f(x, y) = 0? Provide both the equation and sketch of the shape with appropriate labels. (b) Sketch some contours of the function and indicate the direction of elevation increase and direction of elevation decrease. (c) Suppose a hiker is following the trail at the point (-1, -1), walking in the direction of largest elevation gain. What is the slope of the mountain in the direction the hiker is taking? (d) Suppose the hiker at the point (-1, -1) decides to leave the mountain. Which direction (given by a vector) should the hiker travel to decrease their elevation as fast as possible?2. (10 points) Given f(r, y) = In(x2 + y), answer the following questions: (a) Explain in one or two sentences why f(r, y) is differentiable at the point (2, 3). (b) Determine the equation of the tangent plane at the point (2, 3)