Ill take it from the top please excuse me for any misspellings. In Numerical analysis, I have to show that a function only converges towards a solution in a certain interval. The function is f(x)=x/8+arctg(x) Im using Newtons method, i.e. xk+1 = xk - f(x)/f'(x) And i know it will converge if I am in an interval that satisfies |xk-xk+1| < 2xk I then use that f(x)/f'(x) < 2xk giving me 1+8*arctg(x)/x --------------- < 2 1+8/1+x^2 My problem is now how to solve this inequality, i'm trying with mathematica, but i cant make it work Its not important how I solve it, i just need a solution, and guidelines to finding it... Anyone up for the task?