Suppose we know that a twice-differentiable function f(x,y) has its only critical point at (-2,1), and that furthermore fr.(-2,1) = 8 and f(-2, 1) = 4. What need be true about fwy so that has a saddle point at (-2, 1)? Is it possible for f to have a relative maximum at (-2, 1)? What about a relative minimum?
