Which of the Following Is (Are) True Of $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 3 x ?$

question 31

Multiple Choice

Which of the following is (are) true of $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 3 x ?$
(I) f increasing on (1, ?)
(II) (1, 1) is a relative extreme point
(III) (1, 1) is an inflection point
(IV) f is concave up on (-?, 1)

• A) II, III, and IV
• B) I and III
• C) I, II, and IV
• D) I, II, and III
• E) all of these

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Definitions:

Rival in Consumption

A good or service is considered a rival in consumption if its use by one individual diminishes the availability or quality for others.

Whales

Large aquatic mammals known for their size, intelligence, and complex social structures, belonging to the order Cetacea.

Types of Goods

Classification of goods based on characteristics such as excludability, rivalry in consumption, and the nature of the product (e.g., public goods, private goods, club goods).

Free-Ride

To benefit from a resource, good, or service without providing fair compensation or contribution.