Most "linear" part of a function

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I have an electricity problem in which I have to determine de most linear part of a function. I want to know if there is a way that I could determine this range via linear regression, differential calculus, or other. The function is $$f(x)=k\frac{x}{1-x} $$ for $x>0$ and $k$ constant. I do not study mathematics so thats why i come here, thanks in advance.