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Extrema of a Bivariate Function

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Find the extrema of f subject to the stated constraints.

f(x,y) = x - y,

subject to

x^2 - y^2 = 2

© BrainMass Inc. brainmass.com October 24, 2018, 10:47 pm ad1c9bdddf
https://brainmass.com/math/computing-values-of-functions/extrema-bivariate-function-170743

Solution Preview

First lets get the function all in terms of x.

Looking at the constraint:
y^2 = x^2 - 2
y = sqrt(x^2 - 2)

Plugging this into f(x,y) we get:

f(x,y) = x - y = x - sqrt(x^2 - 2)

In order to find extrema of a function we take it's ...

Solution Summary

Extrema of a bivariate function are located. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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