{"id":4473,"date":"2013-12-24T06:05:19","date_gmt":"2013-12-23T21:05:19","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=4473"},"modified":"2014-08-01T19:07:55","modified_gmt":"2014-08-01T10:07:55","slug":"method-of-lagrange-multipliers","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4473","title":{"rendered":"Method of Lagrange multipliers"},"content":{"rendered":"
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Sometimes you may wish to find the relative maxima or minima of f(x, y)<\/span> = 0 subject to some constraint condition φ(x, y)<\/span> = 0. To do this, form the function h(x, y)<\/span> = f(x, y)<\/span> + λφ(x, y)<\/span> and set <\/p>\n

\\displaystyle \\partial h\/\\partial x = 0,\\ \\partial h\/\\partial y = 0<\/p>\n

The constant λ is called a Lagrange multiplier<\/span> and the method is called the method of Lagrange multipliers<\/span>. <\/p>\n<\/blockquote>\n