Extrema with Lagrange in Vector Calc.

[DougD720]

I know this is supposed to go in the HW forum but its not working there so I'm trying it here, and I'm actually running into the same problem with another problem AGAIN. Someone tell me if I am doing this right:

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$$\nabla$$

Homework Statement

Find the extrema of f(x,y)=x-y ; subject to x²-y²=2

Homework Equations

$$\nabla$$f=$$\lambda$$$$\nabla$$g

The Attempt at a Solution

$$\nabla$$f=(1,-1)
$$\nabla$$g=(2x, -2x)

(1,-1)=$$\lambda$$(2x, -2x)

1 = $$\lambda$$(2x) |-> $$\lambda$$=$$\frac{1}{2x}$$
-1 = $$\lambda$$(-2y) |-> $$\lambda$$=$$\frac{1}{2y}$$

Which means x = y , but it has to satisfy x²-y²=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 parallel 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.



Thanks for the help!

 

[DougD720]

Nevermind... it said there was an error but it did post it in the HW forums... so if someone could delete this i'd appreciate it :)