Can anyone explain this solution (contractive function, interval, first derivative related) – math.stackexchange.com

Can anyone explain this solution (contractive function, interval, first derivative related) – math.stackexchange.com

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We are trying to find a positive null $x \geq 0$ of $$f(x) = \sqrt{x+1}+\frac{\text{sin}(x)}{10}-2$$ Choose $X=\left[0,8\right]$. For $x \in X$ we have that $$\frac{1}{15}= ...

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