Find the points on the curve `y=x^3`at which the slope of the tangent is equal to the y-coordinate of the point.

Explanation

To find the points on the curve \( y = x^3 \) where the slope of the tangent is equal to the y-coordinate of the point, we can follow these steps:

### Step 1: Define the point on the curve
Let the point on the curve be \( ( \alpha, \beta ) \). Since the point lies on the curve \( y = x^3 \), we have:
\[ \beta = \alpha^3 \tag{1} \]

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