Hi

Let f(x) = cos(3x)-2x+1 with a representative curve Cf

Start from say

Then is the abscissa of the intersection point between the x axis and the tangent to the curve Cf at the point whose abscissa is

f'(x) = -3 sin(3x)-2

The equation of the tangent to Cf at the point of abscissa is

is given by

Start for example from and then use a calculator to iterate and find the best estimation of the solution