- #1

- 327

- 1

## Homework Statement

Find all points on the surface at which the tangent plane is horizontal

z=x

^{3}y

^{2}

Things I know:

Tangent plane is horizontal then therefore the normal must be vertical in order to be perpendicular.

Dot product of the tangent plane with normal is = 0

Normal plane is given by the partial with respect to x,y,z evaluated at some points P(x

_{0},y

_{0},z

_{0})

Putting that together I get

f(x,y,z)=x

^{3}y

^{2}-z

f

_{x}=3x

^{2}y

^{2}

f

_{y}=2x

^{3}y

f

_{z}=-1

Here is where I am completely stuck I know that I still don't have a normal vector because I do not have any points to plug in to the partials.