Suppose ( 1,1 ) is a critical point of a function \( f \) with continuous second derivatives. In each case, what can you say about \( ? \)
(a) \( f_{x x}(1,1)=1, f_{x y}(1,1)=2, f_{y y}(1,1)=7 \)
The critical point \( (1,1) \) is a local minimum.
The critical point \( (1,1) \) is a local maximum.
The critical point \( (1,1) \) is a saddle point.
Nothing can be determined about the critical point \( (1,1) \).
(b) \( f_{x x}(1,1)=1, f_{x y}(1,1)=4, f_{y j}(1,1)=7 \)
The critical point \( (1,1) \) is a local minimum.
The critical point \( (1,1) \) is a local maximum.
The critical point \( (1,1) \) is a saddle point.
Nothing can be determined about the critteal point \( (1,1) \).
