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:

Autotroph

Producer. Organism that makes its own food using energy from the environment and carbon from inorganic molecules such as carbon dioxide.

Chemical Energy

A form of potential energy stored in the bonds of chemical compounds, released during chemical reactions.

Photorespiration

A process in plant metabolism where oxygen is consumed and carbon dioxide is released, typically reducing the efficiency of photosynthesis.

C4 Plants

Plants that utilize the C4 carbon fixation pathway, enabling them to photosynthesize more efficiently in high light and temperature conditions than C3 plants.