Answer :

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).


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