Find the equations of all lines having slope 0 which are tangent to the curve

Question

Philoid · Accepted Answer

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 0, then we get,

⇒ -2(x-1)=0

⇒ x =1

So, when x = 1 then y =

Now, the equation of the tangent (0,) is given by:

y – = 0(x-1)

⇒ y - = 0

⇒ y =

Therefore, the equations of the required line is y = .