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Lagrange Multipliers
Ok, I'm having a problem understanding a question about Lagrange Multipliers.
Given the function f(x, y) = 16 − x2 − y2 and the constraint (x − 1)2 + (y − 1)2 = 4, find the maximum and minimum. I've reduced it to the system:
There are a few ways to solve this:
I know that the real answer is when x = y, but I can't get that going forwards. Anyone have suggestions as to how to approach it? |
Re: Lagrange Multipliers
1. and 2. of your system are incorrect. The left hand side is correct, but the right hand side is wrong. What is the derivative of (x-1)^2 with respect to x? Ditto (y-1)^2 w.r.t. y. You might try fully expanding the expression and then deriving it if you're still getting 2x and 2y.
Hint: The chain rule always applies in derivatives, everywhere, all the time. |
Re: Lagrange Multipliers
Quote:
Ok, it doesn't. Just 2(x - 1) instead. It's always the little things. |
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