Find the Maximum and Minimum Values of the Function $f ( x , y ) = x y$

question 162

Essay

Find the maximum and minimum values of the function $f ( x , y ) = x y$ on the ellipse given by the equation $x ^ { 2 } + \frac { y ^ { 2 } } { 4 } = 1$ .

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Definitions:

Probabilities

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

Coin Toss

A simple randomness procedure used to decide between two equally probable outcomes with the flip of a coin.

Expected Value

The predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence.

Expected Value

An average value determined by weighing all potential outcomes of a random variable according to their likelihood of happening.