For a function z = (x, y), suppose that the point (a, b) has been identified such

For a function z = ƒ(x, y), suppose that the point (a, b) has been identified such that ƒ_x(a, b) = ƒ_y(a, b) = 0. We can conclude that a relative maximum or a relative minimum must exist at (a, b).

Determine whether each of the following statements is true or false, and explain why.