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

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April 23

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

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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 (talkcontribs) 21:12, 23 April 2015 (UTC)[reply]

You substituted in the values incorrectly.   has value   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)[reply]