Question $5f(x,y,z)=y{x}^2+z{y}^2+z^2-2yx-2zy+y+z$

$a.$ Find all the critical point$(s)of$ this function.

$b.$ Find the Hessian matrix.

$c.$ Classify onle ONE $of$ the critical point$(s)of$ your choice.

$5\mathrm{.}2$ Find all the values for $kso$ that $f(x,y)=x^4-kxy+y4$ has a local

minimum $at(1,1).$ Give your answer $in$ the form $ofan$ interval.

$5\mathrm{.}3$ Find the maximum and minimum values $of$ the function $f(x,y,z)=$

$x^2+y^2+z^2$ subject $to2x+2y-4z=0$ and $4x-2y+2z=0$