Q8 of 149 Page 16

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)


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