Find and Classify the Relative Extrema and Saddle Points of the Function

question 32

Multiple Choice

Find and classify the relative extrema and saddle points of the function $f ( x , y ) = e ^ { - 2 x } \sin 4 y$ for $x \geq 0$ and $0 \leq y \leq \frac { \pi } { 2 } .$

• A)
• None
• B)
• Relative maximum \(f \left( 0 , \frac { \pi } { 8 } \right) = 1\)
• C)
• Saddle point \(( 0,0,0 )\)
• D)
• Relative minimum \(f \left( 0 , \frac { \pi } { 4 } \right) = 0\)

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Definitions:

Self-regulation

The ability of an individual to manage their emotions, thoughts, and behaviors in accordance with long-term goals.

Social Referencing

Understanding an ambiguous situation by seeking another person’s perception of it.

Stranger Anxiety

A developmental situation where infants begin to exhibit distress or wariness in the presence of unfamiliar people.

Mutual-regulation Model

A theory suggesting that individuals in relationships manage and adjust their emotions and behaviors in response to each other.