5. Let V be open in R 2,

(a,

b) E V, and f : V ---+ R have second-order partial derivatives on V with fx

(a,

b) = fy

(a,

b) = O. If the second-order partial derivatives of f are continuous at

(a,

b) and exactly two of the three numbers fxx

(a, b), fxy

(a, b), and fyy

(a,

b) are zero, prove that

(a,

b) is a saddle point if fxy

(a,

b) =I- O.