Q16. Consider the function z = f(r, y) = 12 + 16y? + 4. (a) [2 points] What is the domain and range of f ? Briefly justify your answer. (b) [2 points] Draw a contour diagram for f with the level curves k = f(x, y) for k = 4 and k = 20. Show your work and indicate the value of & corresponding to each curve in your diagram. Do not forget the scales on the coordinate axes, and choose the scales so that the curves can be properly drawn and seen. (c) [1 point] Sketch the trace of f in the rz-plane. (d) [2 points] Find the directional derivative of f in the direction of the vector v = (3, 4) at the point (x, y) = (5, 1). Show all your work