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Homework Statement
Find the extrema of f subject to the stated constraint:
f(x,y) = x-y subject to x2-y2=2
Homework Equations
Apply the Lagrange Multiplier!
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) = x2-y2-2
Now let L(x,y) = f-[tex]\lambda[/tex]g (where [tex]\lambda[/tex] = the Lagrange Multiplier)
Lx = 1 - 2[tex]\lambda[/tex]x = 0
Ly = -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) = x2-y2-2 = 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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