\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f : [0, 1] \to [0, 1]\), \(f(x) = (x + 2)/(x + 3)\). Show that \(f\) is stable on \([0, 1]\), that \(|f'| \le 1/9\) on \(]0, 1[\), and conclude that \(f\) admits a unique fixed point \(\ell \in [0, 1]\). (You may use the contraction-principle recipe from the cours Method M5.1.)
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