The Function $f ( x ) = \frac { 1 } { 3 } x ^ { 3 } - 25 x$

question 19

Multiple Choice

The function $f ( x ) = \frac { 1 } { 3 } x ^ { 3 } - 25 x$ satisfies the hypotheses of Rolle's Theorem on the interval $[ 0,5 \sqrt { 3 } ]$ . Find all values of $c$ that satisfy the conclusion of the theorem.

• A) \(\pm 5\)
• B) 5
• C) \(\pm 4\)
• D) 4

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Definitions:

Probability Distribution

A representation of the likelihood of different outcomes in an experiment.

Foreclosed

A legal process in which a lender takes control of a property after the owner fails to make mortgage payments, leading to the loss of the property by the owner.

Vickrey Auction

An auction in which bids are submitted secretly, with the item being awarded to the top bidder who then pays the amount bid by the second-highest bidder.

Willingness To Pay

The maximum amount an individual is prepared to spend to procure a good or service, reflecting the value they place on it.