Find the equation of the normals to the curve y = x ^3 + 2x + 6 which are parallel to the line x + 14y + 4 = 0.
Find the equation of the normals to the curve y = x ^3 + 2x + 6 which are parallel to the line x + 14y + 4 = 0.

Equation of the curve  ….(i)

  Slope of the tangent at 

 Slope of the normal to the curve at 

……….(ii)

But Slope of the normal (given) = 

  = 

  

 

 

 

 From eq. (i), at 

at 

Therefore, the points of contact are (2, 18) and 

 Equation of the normal at (2, 18) is 

 

 

And Equation of the normal at  is