Testwiki:Reference desk/Archives/Mathematics/2015 April 23

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April 23

I think there might be an error in the Lagrange Multiplier article

There might be an error in example 2 in the "Lagrange Multiplier" Wikipedia article. The article says that the maximum occurs at Template:Nowrap. This point falls on the circle Template:Nowrap and gives a value Template:Nowrap. But the point Template:Nowrap also meets the constraint and gives a value Template:Nowrap. This is larger than sqrt(2). Doesn't this show that the answer given in the example is not a maximum? — Preceding unsigned comment added by Wthurt (talk • contribs) 21:12, 23 April 2015 (UTC)

You substituted in the values incorrectly. $x^{2}y$ has value $\frac{3}{2}\sqrt{\frac{3}{2}}$ at your suggested critical point, but at the maximums the function attains the value 2, which is greater than at the point you suggested.--Jasper Deng (talk) 00:05, 24 April 2015 (UTC)