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

question 106

Multiple Choice

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 \(( 1,1 )\)

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