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)

step-by-step explanation:

a child is 12 years old, and his father is 32 years older. in how many years will the age of the father be 2 times the age of the child?

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this needs to be the answer format, or else your answer is incomplete.

if the number of years is x, then the equation is

in __ years