Consider the three points $(2,3)$, $(0,4)$, and $(6,6)$.

(a) Supposed that at $(2,3)$, we know that $f_x=f_y=0$ and $f_{xx} > 0$, $f_{yy} = 0$, and $f_{xy} > 0$. What can we conclude about the behavior of this function near the point $(2,3)$? ? (2,3) is a local maximum (2,3) is a local minimum (2,3) is a saddle point (2,3) is a none of these

(b) Supposed that at $(0,4)$, we know that $f_x=f_y=0$ and $f_{xx} < 0$, $f_{yy} < 0$, and $f_{xy} = 0$. What can we conclude about the behavior of this function near the point $(0,4)$? ? (0,4) is a local maximum (0,4) is a local minimum (0,4) is a saddle point (0,4) is a none of these

(c) Supposed that at $(6,6)$, we know that $f_x=f_y=0$ and $f_{xx} = 0$, $f_{yy} = 0$, and $f_{xy} < 0$. What can we conclude about the behavior of this function near the point $(6,6)$? ? (6,6) is a local maximum (6,6) is a local minimum (6,6) is a saddle point (6,6) is a none of these

Using this information, on a separate sheet of paper sketch a possible contour diagram for $f$.