4x 1. Consider the surface z = f(x,y) - a. 3 pts On the axes provided, draw the level curve of f(x,y) that passes through the point (x,y)=(2,-2). X b. 3 pts A bug is on the surface off at the point (x,y) = (2,-2). In which direction (as a vector in 2 space) should the bug go to climb the steepest route possible? c. 3 pes What is the slope the bug will encounter when he moves from the point (x,y) = (2,-2) in the direction of the steepest climb? d. 2 pts On the sketch from part a, draw the gradient vector of fat the point (x, y) = (2,-2). e. pes The bug decides to travel on the surface from the point (x, y) = (2,-2) toward the point (x, y) = (-2,1). What is the slope of the bug's path as it leaves the point (x,y) = (2,-2) in this direction? Give an exact answer. at the point (x, y) = (2,-2). 4x f. pts Find the equation of the plane tangent to the surface z = S(x,y) = Circle your answer. g. 3 pts The bug flies off of the surface from the point (x, y) = (2,-2) in a direction that is normal to the surface, where the bug's z-value increases. In what direction is the bug flying? Give your answer as a vector in 3-space