Etude complète d'une fonction simple

f(x) = (x - 2)/(3 x - 2)

a) Dom f =  \\ {2/3}

b) Limites et asymptotes

2 \!\(lim\+\(x\( → \+ > \) - \)\) f(x) = -∞ 3

2 \!\(lim\+\(x\( → \+ < \) - \)\) f(x) = ∞ 3

AV ≡ x = 2/3

lim f(x) = lim f(x) = 1/3 x→ +∞ x→ -∞

AH ≡ y = 1/3

c) Etude de f

x |      2/3      2     
(x - 2)/(3 x - 2) | + | - 0 +

d) Dérivée

f'(x) = 4/(2 - 3 x)^2

x |      2/3     
4/(2 - 3 x)^2 | + | +

e) Dérivée seconde

f\"(x) = 24/(2 - 3 x)^3

x |      2/3     
24/(2 - 3 x)^3 | + | -

f) Graphe de f

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Créé avec Mathematica  (Mars 26, 2006)
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