H(x,y)=[} (partial ^2f)/(partial x^2)&(partial ^2f)/(partial xpartial y) (partial ^2f)/(partial ypartial x)&(partial ^2f)/(partial y^2) ] Calculando as derivadas de segunda ordem: (partial ^2f)/(partial x^2)=6x, (partial ^2f)/(partial y^2)=2, (partial ^2f)/(partial xpartial y)=(partial ^2f)/(partial ypartial x)=0

matriz Hessiana $H(x,y)$ é dada por:<br /><br />$H(x,y)=[\begin{matrix} \frac {\partial ^{2}f}{\partial x^{2}}&\frac {\partial ^{2}f}{\partial x\partial y}\\ \frac {\partial ^{2}f}{\partial y\partial x}&\frac {\partial ^{2}f}{\partial y^{2}}\end{matrix} ]$<br /><br />Substituindo as derivadas de segunda ordem fornecidas, temos:<br /><br />$H(x,y)=[\begin{matrix} 6x&0\\ 0&2\end{matrix} ]$<br /><br />Portanto, a matriz Hessiana $H(x,y)$ é:<br /><br />$H(x,y)=[\begin{matrix} 6x&0\\ 0&2\end{matrix} ]$