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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Definitions:

Human Logic

The process of reasoning and thinking that is characteristic of the human mind, including the ability to draw inferences and make conclusions based on information.

First Alternative

The initial solution or option considered in decision-making or problem-solving processes.

Consultative Decisions

Decision-making processes where input or feedback is sought from others, especially those who will be affected by the decision, before a final choice is made.

5-Step Process

A structured approach to problem-solving or project management, typically involving stages such as planning, implementation, and evaluation.