1-Over what domain the function strictly convex?

2-Give a linear and quadratic approximations for this function at the point

3-Are these approximations convex, concave or neither?

Thank you very much.

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- January 2nd 2009, 09:14 AMabstarConvexity, concave
1-Over what domain the function strictly convex?

2-Give a linear and quadratic approximations for this function at the point

3-Are these approximations convex, concave or neither?

Thank you very much. - January 2nd 2009, 10:04 AMLast_Singularity
- January 2nd 2009, 10:58 AMabstar
What about the Hessian matris in looking for the convexity.

As far as i know, If the Hessian matrice is positive definite: the function is strictly convex, If it is positive semidefinite it is convex. And if the Hessian is negative than concave. Am i right?