Find the critical points and classify them $($local minimum, local maximum, or saddle point$)$ for the function: $f(x,y)=x^3+y^3-3xy.$

Find the critical points and classify them $($local minimum, local maximum, or saddle point$)$ for the function: $h(x,y)=x^{2}y+y^{2}x-x^3-y^3.$

Find the critical points and classify them $($local minimum, local maximum, or saddle point$)$ for the function: $h(x,y)=x^4+y^4-4x^2-4y^2+6.$

Find the critical points and classify them $($local minimum, local maximum, or saddle point$)$ for the function: $l(x,y)=x^3-3x+y^4-4y^2.$