Find an Equation of the Tangent Line to the Curve $y = 8 \arccos \left( \frac { x } { 2 } \right)$

question 57

Multiple Choice

Find an equation of the tangent line to the curve $y = 8 \arccos \left( \frac { x } { 2 } \right)$ at the point $( 1 , \pi )$ .

• A) \(y = \frac { \sqrt { 8 } } { 3 } x + 6 \pi - \frac { \sqrt { 8 } } { 3 }\)
• B)\(y = - \frac { \sqrt { 3 } } { 8 } x + \pi + 6 \frac { \sqrt { 3 } } { 8 }\)
• C)\(y = - \frac { 8 } { \sqrt { 3 } } x + \pi + \frac { 8 } { \sqrt { 3 } }\)
• D)\(y = \frac { 8 } { \sqrt { 3 } } x + 3 \pi - \frac { 8 } { \sqrt { 3 } }\)
• E)\(y = \frac { \sqrt { 3 } } { 8 } x + \pi - 6 \frac { \sqrt { 3 } } { 8 }\)

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Definitions:

Observational Learning

A process in which an individual learns new responses by observing the behavior of another (a model) rather than through direct experience; sometimes called vicarious conditioning.

Classical Conditioning

A learning process that occurs when two stimuli are repeatedly paired; a response that is at first elicited by the second stimulus is eventually elicited by the first stimulus alone.

Operant Conditioning

A method of learning that occurs through rewards and punishments for behavior, aiming at the strengthening or weakening of voluntary behaviors.

Social-Cognitive Learning

A theory that suggests learning occurs through observation, imitation, and modeling, influenced by both environmental and cognitive factors.