Wikipedia: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 (±sqrt(2), 1). This point falls on the circle (x^2 + y^2 = 3) and gives a value x^2 * y = sqrt(2). But the point (sqrt(3/2) , sqrt(3/2)) also meets the constraint and gives a value x^2*y = 1.5. 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)