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

question 86

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 \(( 0,0,0 )\)
• \(\mathrm { d } .\) Relative minimum \(f \left( 0 , \frac { \pi } { 4 } \right) = 0\)

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Definitions:

Emotionally Charged

Referring to situations or subjects that evoke strong emotional responses.

Complexes

A collection of thoughts, feelings, attitudes, and memories that focus on a particular concept, often unconsciously influencing behavior.

Supraordinate

A term typically used in social psychology to describe a group identity that transcends the smaller group identifications of its members, promoting broader social unity.

Inner Polarities

Refers to the opposing forces or tendencies within a person's psyche or character, often related to personality aspects that individuals struggle to reconcile or balance.