Use the Function Below and Its Derivative to Determine Any $f$

question 14

Multiple Choice

Use the function below and its derivative to determine any points on the graph of $f$ at which the tangent line is horizontal.
$f(x) =3 x^{4}-6 x^{2}, f^{\prime}(x) =12 x^{3}-12 x$

• A) \( (-1,-3),(0,0),(1,-3) \)
• B) \( (-1,3),(1,12) \)
• C) \( (-1,-3),(1,-3) \)
• D) \( (0,0),(1,0) \)
• E) \( (0,0),(1,-3) \)

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Definitions:

Imaginal System

A psychological concept referring to the capacity of the mind to imagine, visualize, or create mental images.

Mental Picture

A visual representation in the mind of objects, people, or situations that are not currently being viewed.

Imitation

The action of copying or reproducing someone else’s behavior, actions, or expressions, often as a method of learning or social interaction.

Encode

The process of converting information into a form that can be stored in the memory, such as transforming thoughts into language.