Q6 of 149 Page 16

Find a point on the curve y2 = 2x3 at which the Slope of the tangent is 3

Given:


The curve y2 = 2x3 and The Slope of tangent is 3


y2 = 2x3


Differentiating the above w.r.t x


⇒ 2y2 – 1 = 2x3 – 1


⇒ y = 3x2


⇒


Since, The Slope of tangent is 3


= 3


⇒ = 1


⇒ x2 = y


Substituting x2 = y in y2 = 2x3,


(x2)2 = 2x3


x4 – 2x3 = 0


x3(x – 2) = 0


x3 = 0 or (x – 2) = 0


x = 0 or x = 2


If x = 0


⇒


⇒ , which is not possible.


So we take x = 2 and substitute it in y2 = 2x3,we get


y2 = 2(2)3


y2 = 28


y2 = 16


y = 4


Thus, the required point is (2,4)


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