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

question 39

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:

Trend Line

A line graphed in a scatter plot to show the general direction of a dataset over time.

Quarterly Data

Data that is collected, reported, or compiled at three-month intervals, often used in financial and economic analysis to track seasonal patterns and short-term trends.

Seasonal Indexes

Numerical values that represent the relative level of seasonal influence on a variable, often used to adjust data for seasonal effects.

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Data that has been modified to remove effects of seasonal patterns to provide a clearer view of non-seasonal trends.