Graph the Equation $y = x \sqrt { 7 - x ^ { 2 } }$

question 305

Multiple Choice

Graph the equation. Include the coordinates of any local and absolute extreme points and inflection points.
- $y = x \sqrt { 7 - x ^ { 2 } }$

• A) local minimum: \(\left( - \frac { \sqrt { 14 } } { 2 } , - \frac { 7 } { 2 } \right)\) local maximum: \(\left( \frac { \sqrt { 14 } } { 2 } , \frac { 7 } { 2 } \right)\) inflection point: \(( 0,0 )\)
• B) local maximum: \(\left( \frac { 14 } { 3 } , \frac { 2 \cdot 7 ^ { 3 / 2 } \cdot \sqrt { 3 } } { 9 } \right)\) \(\text { no inflection point. }\)
• C) local maximum: \(( 0 , \sqrt { 7 } )\) no inflection points.
• D) local minimum: \( \left(-\frac{\sqrt{21}}{3},-\frac{2 \cdot 7^{3 / 2} \cdot \sqrt{3}}{9}\right) \) local maximum: \( \left(\frac{\sqrt{21}}{3}, \frac{2 \cdot 73 / 2 \cdot \sqrt{3}}{9}\right) \) inflection point: \( (0,0) \)

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Definitions:

Passions

Intense emotions or desires that drive individuals to pursue specific interests or activities.

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The natural rhythm of sleep and wakefulness, indicating when and how long a person sleeps, which can vary by age and lifestyle.

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A phase of sleep characterized by rapid eye movements, dreaming, and increased brain activity.

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A stage of sleep characterized by slow brain waves, known as delta waves, associated with physical renewal and repair.