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

Question

Quizplus · Accepted Answer

Since $f _ { x x } (1,1) > 0$, $(1,1)$ is a local minimum or a saddle point. Since the determinant of the Hessian matrix is positive, we know that $f$ has a local minimum at $(1,1)$.

Suppose (1,1)( 1,1 )(1,1) Is a Critical Point of a Function fff

Suppose $( 1,1 )$ Is a Critical Point of a Function $f$