Problem # $5$: Find the points on the graph of $f(x,y)=(y+6)(x-3{)}^5$ at which the tangent plane

is horizontal.

$($A$)$ All points on the line $r(t)=($:$t,0,0$:$)$

$($B$)$ All points on the line $r(t)=($:$t,-6,0$:$)$

$($C$)$ All points on the line $r(t)=($:$0,t,0$:$)$

$($D$)$ All points on the line $r(t)=($:$3,t,0$:$)$

$($E$)$ The point $(3,-6,0)$ only

$($F$)$ The point $(-6,3,0)$ only

$($G$)$ All points on the line $r(t)=($:$t,3,0$:$)$

$($H$)$ All points on the line $r(t)=($:$-6,t,0$:$)$