$(10$ points$)$ Let $f(x,y)=y-xy-y^2,P=(1,2)$ and $Q=(-2,0).$

$($A$)$ Find the gradient vector of the function at $P.($solution$)$

$($B$)$ Parameterize the intersection of the surface defined by the function and $x=1.($solution$)$

$($C$)$ Parameterize the tangent line at $(P,f(P))$ to the intersection you found above. $($solution$)$

$($D$)$ Use a tangent plane to approximate $f(1\mathrm{.}1,1\mathrm{.}8).($solution$)$