Find the point on the curve `y=x^2` where the slope of the tangent is equal to the x-coordinate of the point.

Answer

The point is `(0,0)`

Explanation

Let the point be `(x_{1}, y_{1})`.

As per ques:

`y=x^{2}`

Point `(x_{1}, y_{1})` lies on a curve.


`\therefore y_{1}=x_{1}^{2} \ldots(1)`


Now,
$$
y=x^{2} \Rightarrow \frac{d y}{d x}=2 x
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