I'm having a little trouble with another old test question. It states:(adsbygoogle = window.adsbygoogle || []).push({});

Use LaGrange multipliers to find the point on the line 2x + 3y = 3 that is closest to the point P(4, 2).

I assume that my constraint is g(x, y) = 2x + 3y = 3, and I have to come up with a function f(x, y) to be maximized or minimized. I recall part of the solution, and it had to do with constructing a line that goes through the point P(4, 2).

If I went this route, I'd have something like y = 14/3 - 2/3*x from the first equation. I obtained the slope from g(x, y) ---> y = 1 - 2/3*x. Then I would turn y = 14/3 - 2/3*x into a function of x and y ---> f(x, y) = 14/3 - 2/3*x - y = 0 (I'm not even sure if this is mathematically correct). The thing is, once I take the partial derivatives of f and g, I have no x terms and no y terms. I really don't know how to go about finding the solution.

Any help is appreciated.

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# Homework Help: LaGrange Multipliers

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