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 March 19th, 2012, 11:10 AM #1 Newbie   Joined: Mar 2012 Posts: 6 Thanks: 0 Lagrange multiplier (am I doing this right?)? Hi guy's, could someone please tell me if I'm doing this right!? the question that was asked: f (x, y) = 18y + 6x ? 2xy Calculate (by Lagrange multiplier) the stationary points of f(x,y), under the constraint: x ? y� = 0 Also calculate the value of the function at the stationary points and also calculate 'Lagrange multiplier' (?) for the(se) points. So what i did: L(x,y,?)= 18y+6x-2xy-?(x-y�) L'x = 6-2y-?=0 L'y = 18-2x-2?y=0 constraint: x-y�=0 This means: x=y� y= ?x or y=-?x 18-2x-2?y = 0 18-2y�-2?y=0 ?=(18-2y�)/2y = (6-2y)/1 18-2y� = 12y-4y� 18= 12y-2y� This gives me: -2y�+12y-18=0 On this is used the ABC formula which gave me: X(1)= 3 and X(2)= 3. Meaning x = 3 So y=?3 or y=-?3 Corresponding points (3,?3) (3,-?3) I would really really appreciate it if someone could check this for me!! Thank you for your attention p.s. sorry if its a bit messy, and my apologies if i have posted this in the wrong section. March 19th, 2012, 12:05 PM #2 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Lagrange multiplier (am I doing this right?)? To find the extrema of subject to the constraint , solve the system of equations: In our case, we have: and so we solve the system: From the first 2 equations, we see: Substituting for x into the 3rd equation, we get: i) When we have: and and This is the constrained minimum. ii) When we have: and and This is the constrained maximum. March 25th, 2012, 07:14 AM #3 Newbie   Joined: Mar 2012 Posts: 6 Thanks: 0 Re: Lagrange multiplier (am I doing this right?)? Thank you soooooo much Mark!! Can�t thank you enough   Tags lagrange, multiplier Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post MMCS Calculus 3 December 7th, 2013 07:44 AM Brazen Calculus 1 January 15th, 2013 10:29 AM dk1702 Abstract Algebra 1 July 21st, 2010 05:25 AM OSearcy4 Calculus 2 October 16th, 2009 01:44 PM roonaldo17 Calculus 0 November 16th, 2008 11:27 AM

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