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

question 80

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.
$f(x) =3 x^{4}-6 x^{2}, \quad f^{\prime}(x) =12 x^{3}-12 x$

• 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:

Situationism

A theory in psychology that suggests human behavior is greatly influenced by external situational factors rather than by internal traits or motivations.

Fundamental Attribution Error

The tendency for observers to underestimate situational influences and overestimate personal characteristics when explaining others' behaviors.

Actor-observer Effect

The tendency to attribute one's own actions to external factors while attributing others' actions to their character or disposition.

Self-serving Bias

A cognitive bias where individuals attribute their successes to personal factors and their failures to external factors, often to maintain self-esteem.