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I have to employ the newton raphson algorithm to find the positive real roots of f(x)=2xln(X)-1. I need to create a function m-file to do so. This is my first matlab assignment and I'm not really familiar with it. I don't really know how to go about the iteration and I'm not very confident with creating the function either. Any help would be greatly appreciated.

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I would recommend to take a look at Cleve Moler's book Numerical Computing with MATLAB. Particularly in Chapter 4 which deals with finding the roots of functions with numerical methods.
Additionally, you can find a lot of submissions for Newton's Method in FEX.

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