Question:

FInd the equation of the normal lines to the curve $\displaystyle y=x^3-3x $ which is parallel to the line of $\displaystyle 2x+18y-9=0 $

Attempt:

$\displaystyle f'(x)=3x^2-3$

$\displaystyle m=9 $

$\displaystyle x=2 ;y=2 $

$\displaystyle y-2=9(x-2) $

Is my equation correct?

If not please answer in steps

Thank you