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

Explanation

To find the equation of the normals to the curve \( y = x^3 + 2x + 6 \) that are parallel to the line \( x + 14y + 4 = 0 \), we can follow these steps:

### Step 1: Find the slope of the given line
The equation of the line is given as \( x + 14y + 4 = 0 \). We can rewrite this in slope-intercept form \( y = mx + b \).

\[ 14y = -x - 4 \implies y = -\frac{1}{14}x - \frac{4}{14} \]
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