Exercise 12.3.9
\[f(x,y)=x^2y+3x^2+4y-5\] \[f_x=2xy+6x\] \[f_{xx}=2y+6\] \[f_y=x^2+4\]
\[f_{yy}=0\] \[f_{xy}=2x\] \[f_{yx}=2x\]