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

Find the extrema of f subject to the stated constraint:

f(x,y) = x-y subject to x^{2}-y^{2}=2

2. Relevant equations

Apply the Lagrange Multiplier!

3. The attempt at a solution

This question was rather odd... I just did a problem similar to this one, and I got the answer right.

Let g(x,y) = x^{2}-y^{2}-2

Now let L(x,y) = f-[tex]\lambda[/tex]g (where [tex]\lambda[/tex] = the Lagrange Multiplier)

L_{x}= 1 - 2[tex]\lambda[/tex]x = 0

L_{y}= -1 + 2[tex]\lambda[/tex]y = 0

I then solve for x and y.

I get x = [tex]\frac{1}{2\lambda}[/tex] = y

I plugged both of them into the constraint g(x,y) = x^{2}-y^{2}-2 = 0

Both x and y cancels out!!! and so

-2 = 0

I am sure I am doing something wrong because there is an answer! I've checked using an online calculator.

Can anyone please show me what I am doing wrong?

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# Homework Help: Find the extrema of f subject to the stated constraint

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