Determine Whether There Is a Relative Maximum, a Relative Minimum $f ( x , y )$

Multiple Choice

Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient information to determine the nature of the function $f ( x , y )$ at the critical point $\left( x _ { 0 } , y _ { 0 } \right)$ . Given: $\begin{array} { l } f _ { x x } \left( x _ { 0 } , y _ { 0 } \right) = - 1 \\f _ { y y } \left( x _ { 0 } , y _ { 0 } \right) = - 8 \\f _ { x y } \left( x _ { 0 } , y _ { 0 } \right) = 5\end{array}$

A) $\text { relative minimum }$ at $\left( x _ { 0 } , y _ { 0 } \right)$
B) $\text { saddle point }$ at $\left( x _ { 0 } , y _ { 0 } \right)$
C) $\text { relative maximum }$ at $\left( x _ { 0 } , y _ { 0 } \right)$
D) $\text { insufficient information to determine the nature of the function }$ at $\left( x _ { 0 } , y _ { 0 } \right)$