Find the Critical Point(s) of the Function

question 34

Multiple Choice

Find the critical point(s) of the function. Then use the second derivative test to classify the nature of each point, if possible. Finally, determine the relative extrema of the function. ​ ​

• A) and ; saddle point: ; relative maximum value: ​
• B) and ; relative minimum: ; relative maximum value:
• C) and ; saddle point: ; relative minimum value: ​
• D) there are no critical points

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Definitions:

Waking Consciousness

A state of clear, organized alertness to the environment and oneself.

Hyperconsciousness

An intensified state of awareness in which one is overly aware of one's thoughts, emotions, and surroundings, often leading to heightened sensitivity or anxiety.

Circadian Rhythms

Physical, mental, and behavioral changes that follow a daily cycle, primarily responding to light and darkness in an organism's environment.

Suprachiasmatic Nucleus

A small region in the brain’s hypothalamus responsible for controlling circadian rhythms, which are the body's internal biological clock.