Find the Critical Points Of $f ( x , y ) = x ^ { 2 } y e ^ { - \left( x ^ { 2 } + 9 y ^ { 2 } \right) }$

question 26

Essay

Find the critical points of $f ( x , y ) = x ^ { 2 } y e ^ { - \left( x ^ { 2 } + 9 y ^ { 2 } \right) }$ Do this by setting $t = - \left( x ^ { 2 } + 9 y ^ { 2 } \right)$ and optimizing $f ( x , y , t ) = x ^ { 2 } y e ^ { t }$ subject to the constraint $t + x ^ { 2 } + 9 y ^ { 2 } = 0$

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Definitions:

Hourly Earnings

The amount of income earned by an individual per hour of work.

Confidence Interval

A range of values, derived from the sample statistics, that is likely to contain the value of an unknown population parameter.

Standard Deviation

An indicator of the spread or distribution of data points in a set, showing the degree to which these points vary from the average value.

Confidence Interval

A collection of numerical values from sample data, considered likely to include the value of a hidden population parameter.