My Math Forum is this function concave?

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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.

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