Find the Minimum Value of the Function $f ( x , y ) = x y$

question 122

Multiple Choice

Find the minimum value of the function $f ( x , y ) = x y$ subject to the constraint that $x ^ { 2 } + y ^ { 2 } = 2$ .

• A) \(\frac { 1 } { 2 }\)
• B)1
• C) \(\frac { 3 } { 2 }\)
• D).2
• E) \(- \frac { 1 } { 2 }\)
• F) \(- 1\)
• G) \(- \frac { 3 } { 2 }\)
• H) \(- 2\)

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Definitions:

Distribution

In statistics, the arrangement of values of a variable showing their observed or theoretical frequency of occurrence.

Normal Distribution

A bell-shaped distribution characterized by its mean and standard deviation, where the majority of data points are concentrated around the mean.

Quality Control Manager

A professional responsible for ensuring that products meet predetermined standards of quality through testing and inspection processes.

Probability

The measure of the likelihood that an event will occur, represented as a number between 0 and 1.