Question -
Answer -
The equation of the given curve is y = x3.
The slope of the tangent at the point (x, y)is given by,
When the slope of the tangent is equal tothe 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 = 3(3)2 =27.
Hence, the required points are (0, 0) and (3, 27).