Find the values of a which ensure that s is sloping upward

Question

Question: (a) The surface S is given, for some constant a, by

z = 3x² + 4y² - axy

Find the values of a which ensure that S is sloping upward when we move in the positive x-direction from the point (1, 2).

(b) With the values of a from part (a), if you move in the positive y-direction from the point (1, 2), does the surface slope up or down? Explain.