Suppose $\backslash ($ f$($x$,$ y$)=$x y$(1-5$ x$-7$ y$)\backslash ).\backslash ($ f$($x$,$ y$)\backslash )$ has $4$ critical points. List them in increasing lexographic order. By that we mean that $\backslash ((\backslash$mathrm$\{$x$\},\backslash$mathrm$\{$y$\})\backslash )$ comes before $\backslash ((\backslash$mathrm$\{$z$\},\backslash$mathrm$\{$w$\})\backslash )$ if $\backslash (\backslash$boldsymbol$\{$x$\}<mi>\backslash </mi>$boldsymbol$\{$z$\}\backslash )$ or if $\backslash (\backslash$boldsymbol$\{$x$\}=\backslash$boldsymbol$\{$z$\}\backslash )$ and $\backslash (\backslash$boldsymbol$\{$y$\}<mi>\backslash </mi>$boldsymbol$\{$w$\}\backslash ).$ Also, determine whether the critical point a local maximum, a local minimim, or a saddle point. First point $(,).$ Classification: $($local minimum, local maximum, saddle point, cannot be determined$).$ Second point $).$ Classification: $($local minimum, local maximum, saddle point, cannot be determined$).$ Third point $().$ Classification: $($local minimum, local maximum, saddle point, cannot be determined$).$ Fourth point $().$ Classification: $($local minimum, local maximum, saddle point, cannot be determined$).$