Use the Boundedness Theorem to Determine Whether the Polynomial Function $f ( x ) = x ^ { 5 } + 10 x ^ { 4 } - 25 x ^ { 3 } - 10 x ^ { 2 } + 24 x$

question 106

Multiple Choice

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition.
-The polynomial f(x) $f ( x ) = x ^ { 5 } + 10 x ^ { 4 } - 25 x ^ { 3 } - 10 x ^ { 2 } + 24 x$ 24x has no real zero greater than 3.

• A) Yes, the boundedness theorem shows that the polynomial has no real zero greater than 3.
• B) No, the boundedness theorem does not show that the polynomial has no real zero greater than 3.

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Definitions:

Unconditioned Stimulus

In behavioral psychology, a stimulus that naturally and automatically triggers a response without the need for prior learning.

Neutral Stimulus

A stimulus that initially produces no specific response other than focusing attention, before conditioning associates it with an unconditioned stimulus.

Unconditioned Response

An automatic, natural reaction to a stimulus that occurs without any prior learning or conditioning.

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The pleasure and sense of satisfaction experienced after eating, which can be a powerful motivation for food consumption and choices.