The given curve y = x³

Then, the slope of the tangent at the point (x, y) is given by:

We know that, when the slope of the tangent is equal to the y- coordinate of the point,

Then y = 3x²

Also, we have y = x³

⇒ 3x² = x3

⇒ x²(x-3) = 0

⇒ x = 0, x = 3

When x = 0 then y = 0

and when x = 3 then y = 27

Therefore, the required points are (0, 0) and (3, 27).