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

Explanation

Given, curve `y=x^3+2x+6`


line `x+14 y+4=0.`


Let `m` be the slope of tangent of the curve


Let `n` be the slope of normal of the curve


Normal to the curve is parallel to `x+14 y+4=0.`


`n=-1/14`


`y=x^3+2x+6`


`(dy)/(dx)=3x^2+2`


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