Suppose (1, 1) Is a Critical Point of a Function $f _ { x } ( 1,1 ) = 8$

Multiple Choice

Suppose (1, 1) is a critical point of a function f with continuous second derivatives. In the case of $f _ { x } ( 1,1 ) = 8$ , $f _ { x y } ( 1,1 ) = 8$ , $f _ { y y } ( 1,1 ) = 10$ what can you say about f ?

A) f has a local maximum at (1,1)
B) f has a saddle point at (1,1)
C) f has a local minimum at (1,1)