2 A surface has equation \(z = \mathrm { f } ( x , y )\) where \(\mathrm { f } ( x , y ) = x ^ { 2 } \sin y + 2 y \cos x\).
- Determine \(\mathrm { f } _ { x } , \mathrm { f } _ { y } , \mathrm { f } _ { x x } , \mathrm { f } _ { y y } , \mathrm { f } _ { x y }\) and \(\mathrm { f } _ { y x }\).
- Verify that \(z\) has a stationary point at \(\left( \frac { 1 } { 2 } \pi , \frac { 1 } { 2 } \pi , \frac { 1 } { 4 } \pi ^ { 2 } \right)\).
- Determine the nature of this stationary point.