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

question 491

Multiple Choice

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

• A) Yes, the boundedness theorem shows that the polynomial has no real zero greater than 2.
• B) No, the boundedness theorem does not show that the polynomial has no real zero greater than 2.

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Definitions:

Producer Surplus

The difference between what producers are willing to accept for a good or service and what they actually receive, representing their gain.

Producer Surplus

The difference between what producers are willing to accept for a product and the amount they actually receive.

Total Revenue

The overall amount of money generated by a firm from the sale of its goods and services, calculated as the unit price multiplied by the quantity sold.

Total Cost

The sum of the fixed cost and the variable cost of producing a given quantity of output.