Problem #$5$: Find the points on the graph of $f(x,y)=(y+7)x^6$ at which the tangent plane is horizontal.

$($A$)$ All points on the line $r(t)=($:$t,-7,0$:$)$

$($B$)$ All points on the line $r(t)=($:$5,t,0$:$)$

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

$($D$)$ The point $(0,-7,0)$ only

$($E$)$ The point $(-7,0,0)$ only

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

$($G$)$ All points on the line $r(t)=($:$-7,t,0$:$)$

$($H$)$ All points on the line $r(t)=($:$t,5,0$:$)$

Problem #$5$: