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

question 42

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:

Value of the Marginal Product

The additional revenue a firm generates from employing one more unit of input, keeping other inputs constant.

Marginal Productivity

The additional output generated by adding one more unit of a specific input, while holding all other inputs constant.

Marginal Cost

The cost added by producing one additional unit of a product or service, a crucial concept in economics for understanding optimization.

Marginal Product

The increase in output derived from the addition of one unit of a certain input, with all other inputs held steady.