# How to mark interactively specific points in a 3dplot?

I have the following code

f[x_, y_, \[Alpha]_: 0] := x^3 - y^3 + 3 \[Alpha] x y
Manipulate[Plot3D[f[x, y, \[Alpha]], {x, -10, 10}, {y, -10, 10}], {\[Alpha],-5,5, 1}]


and I want to mark the points f[0,0,\[Alpha]] and f[1,-1,\[Alpha]] in the graph. I saw some other questions similar to this one but it doesnt deal with interactive content so in all cases I searched in the forum the solutions have static variables that cant be applied to this case.

I will be glad if some one shows me how to add these points to the graph. Thank you.

The interactivity doesn't really change anything. Just use Show in the standard way:

f[x_, y_, α_: 0] := x^3 - y^3 + 3 α x y;
Manipulate[
Show[
Plot3D[f[x, y, α],
{x, -10, 10}, {y, -10, 10}],
Graphics3D[
{
AbsolutePointSize[15],
Point[{
{0, 0, f[0, 0, α]},
{1, -1, f[1, -1, α]}
}]
}
]
],
{α, -5, 5, 1}
]