# Problem: Concave function of two variables

Problem

Show that \(f\left( x,y \right)=-x^2-y^2\) is strictly concave.

Solution

\[H=\left( \right)\]

\(\left| H \right|=4>0\) and \(f_{xx}^{''}=-2<0\) for all \(x\) : \(f\) is strictly concave.

Problem

Show that \(f\left( x,y \right)=-x^2-y^2\) is strictly concave.

Solution

\[H=\left( \right)\]

\(\left| H \right|=4>0\) and \(f_{xx}^{''}=-2<0\) for all \(x\) : \(f\) is strictly concave.