Consider the following function f(x, y) = x² + 4y² + 5. (a) Determine the domain and the range of the function f? Briefly justify your answer. (b) Plot the level curves f(x, y) = k for k = 5 and k = 9. Show your work and indicate the value of k corresponding to each contour on your figure. Do not forget the scales on the coordinate axes, and choose the scales so as to curves can be properly drawn and seen. (c) Draw the trace of f in the xz plane. (d) Find the directional derivative of f at the point (x, y) = (1, 6) in the direction of vector v = 4, 3. Show off all your hard work!