Find the Equation of the Tangent Line to the Curve $x = 3 \pi / 4$

question 3

Multiple Choice

Find the equation of the tangent line to the curve given by f(x) = x sin x at the point $x = 3 \pi / 4$ .

• A) \(y + \frac { \pi \sqrt { 2 } } { 8 } = \frac { \sqrt { 2 } } { 2 } \left( \frac { 3 \pi } { 4 } - 1 \right) \left( x - \frac { 3 \pi } { 4 } \right)\)
• B) \(y - \frac { \pi \sqrt { 2 } } { 8 } = \frac { \sqrt { 2 } } { 2 } \left( \frac { 3 \pi } { 4 } + 1 \right) \left( x - \frac { 3 \pi } { 4 } \right)\)
• C) \(y - \frac { \pi \sqrt { 2 } } { 8 } = - \frac { \sqrt { 2 } } { 2 } \left( \frac { 3 \pi } { 4 } + 1 \right) \left( x - \frac { 3 \pi } { 4 } \right)\)
• D) \(y - \frac { \pi \sqrt { 2 } } { 8 } = - \frac { \sqrt { 2 } } { 2 } \left( \frac { 3 \pi } { 4 } - 1 \right) \left( x - \frac { 3 \pi } { 4 } \right)\)

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Definitions:

Stripped Common Shares

Common shares from which certain rights have been removed, typically dividends or voting rights, often used in structured finance transactions.

Residual Dividend Approach

A method where the firm pays dividends from the residual or leftover equity after paying for all capital expenditures and working capital needs.

Debt/Equity Ratio

A financial ratio that measures the relative proportion of shareholders’ equity and debt used to finance a company’s assets.

Capital Investment

Funds invested in a firm or enterprise for the purpose of furthering its business objectives, including acquiring assets and launching new ventures.