Solución

Máximo: $2\sqrt{11}$ en $f\big(\frac{2}{\sqrt{11}}, \frac{6}{\sqrt{11}}, \frac{-2}{\sqrt{11}}\big)$

Mínimo: $-2\sqrt{11}$ en $f\big(\frac{-2}{\sqrt{11}}, \frac{-6}{\sqrt{11}}, \frac{2}{\sqrt{11}}\big)$