Question

Please help me find all points on the surface at which the tangent plane is horizontal.
z=(x^3)(y^2)

Answer 1

\[z=x^3y^2\]

Answer 2

\[F(x,y,z)=x^2y^3-z\]

Answer 3

Gradient of F(x,y,z):
\[<3x^2y^2,2x^3,-1>\]

Answer 4

horizontal plane means the "slope" = 0, you have gradient vector there, just let it =0 and find out value of x, y, z.