Find a point on the curve y = x2 where the Slope of the tangent is equal to the x – coordinate of the point.
Given:
The curve is y = x2
y = x2
Differentiating the above w.r.t x
⇒ = 2x2 – 1
⇒ = 2x ...(1)
Also given the Slope of the tangent is equal to the x – coordinate,
= x ...(2)
From (1) & (2),we get,
i.e,2x = x
⇒ x = 0.
Substituting this in y = x2, we get,
y = 02
⇒ y = 0
Thus, the required point is (0,0)