Find a point on the curve y = x 2 where the Slope of the tangent is equal to the x – coordinate of the point.

Question

Philoid · Accepted Answer

Given:

The curve is y = x²

y = x²

Differentiating the above w.r.t x

⇒ = 2x^{2 – 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)