Suppose (1,1)is a Critical Point of a Function F with Continuous

question 8

Multiple Choice

Suppose (1,1) is a critical point of a function f with continuous second derivatives. In the case of , , what can you say about f ?

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

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Definitions:

Crepitation

The crackling or popping sounds and sensations experienced under the skin and joints or during the movement of certain body parts, often indicative of gas collection or friction.

Bell Palsy

A temporary condition that causes sudden, temporary weakness or paralysis of the facial muscles, typically on one side of the face.

Cephalhematoma

A localized swelling filled with blood, found on the head of a newborn as a result of birth trauma, typically resolving on its own.

Craniosynostosis

A birth defect in which one or more of the fibrous sutures in an infant's skull prematurely fuses, potentially affecting brain growth.