Find all the roots of the given function. use preliminary analysis and graphing to find good initial approximations. f(x)equals=cosine left parenthesis 3 x right parenthesis minus 7 x squared plus 4 xcos(3x)−7x2+4x

The given function is

  f(x)=cos 3x-7 x²+ 4x

f'(x)=-3 sin 3 x-14 x+4

When you will draw the graph of the function , you will find that root of the function lie between (-1,0).

Consider initial root as,

Using Newton method to find the roots of the equation

So, root of the equation is

         =0.1688878

       =0.1689(approx)