Question

Find a point on the curve y = x² where the Slope of the tangent is equal to the x – coordinate of the point.

Answer 1

Given:

The curve is y = x²

y = x²

Differentiating the above w.r.t x

⇒ \(\frac{dy}{dx}\)= 2x^{2 – 1}

⇒ \(\frac{dy}{dx}\) = 2x ...(1)

Also given the Slope of the tangent is equal to the x – coordinate,

\(\frac{dy}{dx}\) = 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)