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 October 19th, 2013, 05:59 AM #1 Newbie   Joined: Sep 2013 Posts: 4 Thanks: 0 is this function concave? is (x1^2+x2^2)^1/2 a concave function? In the lecture today we were going through the lagrangian multiplier and the condition was that the utility function has to be concave. But when I check this function on a 3D graph the function seems convex? Am I missing something? October 28th, 2013, 08:57 AM #2 Newbie   Joined: Oct 2013 Posts: 2 Thanks: 0 Re: is this function concave? If I remember correctly: Concavity requires: Both second derivative negative and hessian determinant negative First derivatives x1*(x1^2+x2^2)^-1/2 x2*(x1^2+x2^2)^-1/2 Second derivatives (x1^2+x2^2)^-1/2 - x1^2(x1^2+x2^2)^-3/2 (x1^2+x2^2)^-1/2 - x2^2(x1^2+x2^2)^-3/2 Positive assuming Assuming x1,x2>0 which is a very natural. Then the second derivatives are positive and they thus don't qualify for a concave function. Tags concave, function 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 AEcon Algebra 1 October 20th, 2013 11:29 AM loveinla Calculus 0 May 15th, 2013 06:56 AM henoshaile Calculus 4 October 29th, 2012 12:32 PM swagatopablo Algebra 0 October 10th, 2012 10:49 PM jefferson_lc Calculus 1 June 12th, 2009 04:04 PM

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