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:

Genetic Drift

A mechanism of evolution that results in random changes in the frequency of alleles within a population over time.

Allele Frequencies

The proportion of different alleles of the same gene within a given population.

Cladistics

Making hypotheses about evolutionary relationships among clades.

Shared Characteristics

Traits or features that are common across a group of organisms, indicating a degree of genetic, structural, or functional similarity.