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

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:

Depersonalization Disorder

A mental disorder characterized by persistent or recurrent feelings of detachment from one’s own body, thoughts, feelings, or surroundings.

Flashbacks

Sudden, intense, involuntary re-experience of past memories or traumatic events, often a symptom of PTSD.

PTSD

Post-Traumatic Stress Disorder, a mental health condition triggered by experiencing or witnessing a terrifying event, characterized by flashbacks, nightmares, and severe anxiety.

Reexperiencing

The involuntary reliving of traumatic events, often a symptom of PTSD.