$[17$ pt$]$ Let $f(x,y)=x^3-x+x{y}^2+y^3,$ and you are given that $(-\frac{1}{\sqrt[\phantom{2}]{B}}*\frac{2}{\sqrt[\phantom{2}]{B}})$ is one of the critical points.

a$.$ Determine the value of $$ and $.$

a$.==$

b$.$ Hence, find all the critical points of $f(x,y).$ Classify each of the critical points: Saddle

b$.$ Critical points and types: point, local maximum or local minimum.$[17$ pt$]$ Let $f(x,y)=x^3-x+x{y}^2+y^3,$ and you are given that $(-\frac{1}{\sqrt[\phantom{2}]{B}}*\frac{2}{\sqrt[\phantom{2}]{B}})$ is one of the critical points.

a$.$ Determine the value of $$ and $.$

a$.==$

b$.$ Hence, find all the critical points of $f(x,y).$ Classify each of the critical points: Saddle

b$.$ Critical points and types: point, local maximum or local minimum.