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?

Thanks,

Joan

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- November 11th 2010, 01:50 PMjuxiNewton Raphson
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?

Thanks,

Joan - November 12th 2010, 12:32 AMEducated
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. - November 12th 2010, 03:42 AMArchie Meade
The Newton-Raphson method finds close approximations to points at which a graph crosses the x-axis.

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