I am trying to determine the real number x with cos(x)=2x, Newton Method with f(x)=cos(x)-2x.
How do I try and solve this?
You are trying to solve
The function is: therefore the derivative is
Newton Raphson method:
Start off with as where you might think the root might be. If you have no idea, start off with and just substitute in the values into the formula to get and so on.
The graph of the function crosses the x-axis when
is a straight line, passing through the origin and having a slope of
is periodic, with a local maximum at and is at
Since when then since is decreasing from
then there is a solution to slightly to the left of
You could use a value of x around for