Identify the Function's Extreme Values in the Given Domain, and Say

question 334

Multiple Choice

Identify the function's extreme values in the given domain, and say where they are assumed. Tell which of the extreme
values, if any, are absolute.
- $h ( x ) = x ^ { 3 } + 3 x ^ { 2 } + 8 x + 2 , \Leftrightarrow < x \leq 0$

• A) local and absolute maximum: 2 at x = 0;
• B) no local extrema; no absolute extrema
• C) local and absolute maximum: 2 at x = 0;.
• D) local and absolute minimum: 1 at x = -1; local and absolute minimum: 1 at x = -1

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Definitions:

Cerebellum

A part of the brain located at the back of the skull, crucial for motor control, coordination, precision, and timing of movements.

Medulla

The first large swelling at the top of the spinal cord, forming the lowest part of the brain, which is responsible for life-sustaining functions such as breathing, swallowing, and heart rate.

Pons

A part of the brain located above the medulla and below the midbrain, playing a crucial role in regulating breathing, communication between different parts of the brain, and sensations such as hearing.

Fine-Motor Movement

Small movements that involve the coordination of small muscle groups, typically in the hands and fingers, such as writing or buttoning a shirt.