(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the extrema of f(x,y)=x-y ; subject to x^{2}-y^{2}=2

2. Relevant equations

[tex]\nabla[/tex]f=[tex]\lambda[/tex][tex]\nabla[/tex]g

3. The attempt at a solution

[tex]\nabla[/tex]f=(1,-1)

[tex]\nabla[/tex]g=(2x, -2x)

(1,-1)=[tex]\lambda[/tex](2x, -2x)

1 = [tex]\lambda[/tex](2x) -> [tex]\lambda[/tex]=[tex]\frac{1}{2x}[/tex]

-1 = [tex]\lambda[/tex](-2y) -> [tex]\lambda[/tex]=[tex]\frac{1}{2y}[/tex]

Which means x = y , but it has to satisfy x^{2}-y^{2}=2 and if x=y then it cannot satisfy this meaning there are no extrema for this set of equations.

Am i right??? I tried working it out with other methods but it just keeps not working, however, i plotted the two equations in 3D on Maple and they do intersect so shouldn't there be extrema? Or is the fact that x-y is a plane paralell to the xy-axis mean that all points are extrema?

We never did a problem like this in class, one with no apparent solution, so i'm confused a bit here.

And i just did another problem where i'm coming up with a solution that doesn't satisfy one of the constraints... ugh... what am i doing wrong???

Thanks for the help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Extrema/LaGrange in Vector Calc

**Physics Forums | Science Articles, Homework Help, Discussion**