Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f$($x$,$ y$)-7$x$27$y$2$;xy $1$ Part $1$ of $6$ We need to optimize f$($x$,$y$)-7$x$27$y$2$ subject to the constraint g$($x$,$ y$)-$xy$-1.$ To find the possible extreme value points, we must use $?$f$=?$ We have Vf$-(14$x$,1414$y Part $2$ of $6$ V f$-$XVg gives us the equations $14$x$-$Ay$,14$y $-$Xx$.$ From the first equation we have $14-1.$ Substituting this value for $?$ into the second equation gives us y$2$ from which we can say that y $=\backslash$pm Part $3$ of $6$ Now, using xy $1$ and y$2-$x$2,$ we get the two possible extreme points $1)$ and $(-1,1$ Part $4$ of $6$ At these points, we have $(1,1)-1414|$ and r$-1,-1)=1414.$ Part $5$ of $6$ To decide whether at these points fis minimal or maximal, we can check the value of fat other points on the constraint curve xy $-1.$ For example, when x $-2,$ we have y $1/2$ f$($x$,$ y$)26$ and we have X which is $($ larger than $14$ Submit Skip $($you cannot come back$)$