Alexander Santiago
09/23/2023 · High School
Soit \( f \) la fonction numérique définie sur \( \mathbb{R} \) par: \( f(x)=x^{3}-3 x-3 \) 1- Etudier les variations de la fonction \( f \) sur \( \mathbb{R} \). 2- Montrer que l'équation \( f(x)=-2 \) admet 3 solutions dans \( \mathbb{R} \).
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1. La fonction \( f(x) = x^3 - 3x - 3 \) est croissante sur \( (-\infty, -1) \) et \( (1, +\infty) \), décroissante sur \( (-1, 1) \), avec des maximums et minimums en \( x = -1 \) et \( x = 1 \).
2. L'équation \( f(x) = -2 \) admet 3 solutions dans \( \mathbb{R} \).
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