Using the second partial derivative test, I have found (-1,1) to be a saddle point but this option is not available in the MCQ. Have I made a mistake?
The person who set the question insists that (-1,1) is a minimum, not saddle, because:
"We are talking about the local situation at the 2 points. Since the y coordinate of the 2 points are the same at y=1, that means we pass a vertical plane through the 3-D surface, so it becomes a 2-D curve in terms of x. So using 2nd derivative test (as stated explicitly in the question), it leads to local minimum. "