$\text { Find the cubic function of the form } f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d \text {, where } a \neq 0 \text { and the }$

question 96

Multiple Choice

$\text { Find the cubic function of the form } f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d \text {, where } a \neq 0 \text { and the }$ coefficients $a , b , c , d$ are real numbers, which satisfies the conditions given below.
Relative maximum: $( 3,0 )$
Relative minimum: $( 5 , - 2 )$
Inflection point: $( 4 , - 1 )$

• A) \(f ( x ) = \frac { 1 } { 2 } x ^ { 3 } - 6 x ^ { 2 } + \frac { 45 } { 2 } x - 27\)
• B) \(f ( x ) = \frac { 1 } { 2 } x ^ { 3 } - 6 x ^ { 2 } + \frac { 41 } { 2 } x - 26\)
• C) \(f ( x ) = \frac { 1 } { 2 } x ^ { 3 } - 6 x ^ { 2 } + \frac { 45 } { 2 } x + 27\)
• D) \(f ( x ) = - \frac { 1 } { 2 } x ^ { 3 } + 6 x ^ { 2 } - \frac { 45 } { 2 } x + 27\)
• E) \(f ( x ) = \frac { 1 } { 2 } x ^ { 3 } - 6 x ^ { 2 } + \frac { 41 } { 2 } x + 26\)

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Definitions:

Queer Theory

A field of critical theory that emerged in the early 1990s, questioning the fixed identities of sex, gender, and sexuality, while challenging normative assumptions in these areas.

Coherent Entity

A system or organization that is unified, consistent, and able to act or be perceived as a single, integrated whole.

Socially Produced

Created or influenced by societal factors, norms, and interactions among individuals or groups.

Academic Orientalism

A critique of Western scholarship about the Eastern world, emphasizing the stereotypical representation and cultural generalization of the "East" by the "West."