Find the Slope of the Tangent to the Curve $y = \sin ^ { 2 } x + \sin 2 x$

question 240

Multiple Choice

Find the slope of the tangent to the curve $y = \sin ^ { 2 } x + \sin 2 x$ when $x = \frac { \pi } { 4 }$ .

• A) \(- \frac { 1 } { 4 }\)
• B) \(- \frac { \sqrt { 2 } } { 2 }\)
• C) \(- \frac { 1 } { 2 }\)
• D)0
• E) \(\frac { 1 } { 2 }\)
• F) \(\frac { \sqrt { 2 } } { 2 }\)
• G)1
• H) \(\frac { 3 } { 2 }\)

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Definitions:

Habitat Loss

The destruction or degradation of natural environments that organisms depend on for survival, often resulting from human activities like deforestation, agriculture, and urban development.

Extinction

The permanent loss of a species or taxonomic group, where no living members of that group exist anymore.

Promoter

A substance that increases the activity of an enzyme or other catalyst, enhancing a chemical reaction.

Non-native Species

Species that are introduced into an ecosystem where they do not naturally occur, often causing harm to the native biodiversity.