Q11 of 168 Page 211

Find the equation of all lines having slope 2 which are tangents to the curve

It is given that equation of the curve y =

Now, slope of the tangent to the given curve at a point (x,y) is:



Now, if the slope of the tangent is 2, then we get,



⇒ 2(x-3)2 = -1


⇒ (x-3)2 =


This is not possible since the L.H.S. is positive while the R.H.S. is negative.


Therefore, there is no tangent to the given curve having a slope 2.


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Find the point on the curve y = x3 – 11x + 5 at which the tangent is y = x –11.

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