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

$($E$)$ Parametertae the line containing $(P,f(P))$ that is perpendicular to the tangent plane in $P$ so the surface defined by the function.

$($iolution$)$

$(7)$ Find the rate of change of the function at $P$ in the direction of $($:$1,1$:$).($selution$)$

$($G$)$ Find the maximum rate of change of the function at $P.($iolution$)$

$($H$)$ If there is any, find a direction at $P$ in which the function value changes at the rate of $-5.$ If not, explain why not.

$($relution$)$

$($i$)$ Find a direction at $P$ in which the function value does not change. $($solution$)$