We consider the function z = f (x, y) = x2 + 25y2 + 5.

(a) Find the domain and range of f. Briefly justify your answer.

(b) Draw the contour lines k = f(x,y) for k = 5 and k = 30. Show your work and indicate the value of k corresponding to each curve in your diagram. Do not forget to put the scales on the coordinate axes, and choose these scales so that the curves can be seen well.

(c) Draw the graph trace of f in the y = 0 plane. (d) [2 points] Calculate the derivative of f at point (x, y) = (7, 2) in the direction of vector v = 3, 4. Show off all your hard work!