If $f ( x ) = 6 \cos x + \sin ^ { 2 } x$

question 8

Multiple Choice

If $f ( x ) = 6 \cos x + \sin ^ { 2 } x$ , find $f ^ { \prime } ( x )$ and $f ^ { \prime \prime } ( x )$ .

• A) \(f ^ { tt } ( x ) = - 6 \cos ( 2 x ) + 2 \cos ( x )\)
• B) \(f ^ { t } ( x ) = - 6 \sin ( x ) + \sin ( 2 x )\)
• C) \(f ^ { t } ( x ) = - 6 \sin ( 2 x ) + \sin ( x )\)
• D) \(f ^ { tt } ( x ) = - 6 \cos ( x ) + 2 \cos ( 2 x )\)
• E) \(f ^ { tt } ( x ) = - 2 \cos ( 2 x ) + 6 \cos ( x )\)

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Definitions:

Oral Stage

In Freudian psychoanalysis, the first stage of psychosexual development during infancy, where the mouth is the focus of libido and satisfaction comes from sucking and swallowing.

Phallic Stage

The period between the third and fourth years when the focus of sexual pleasure shifts to the genitals.

Latency Stage

In psychoanalytic theory, a period in childhood development following the phallic stage, characterized by a decrease in sexual interests and conflicts.

Defense Mechanism

Unconscious mechanisms employed to shield oneself from anxiety generated by thoughts or feelings deemed unacceptable.