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

Let `m` is the slope of tangent of the curve and `n` is the slope of normal to the curve.

Then, `m*n = -1=> n = -1/m`.

As normal to the curve is parallel to line `x+14y+4 = 0`.

So, their slope will also be equal.

`:. n = -1/14`.

Now, equation of the curve,

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

Differentiating it w.r.t. `x`,

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