Etude de fonction

f(x) = x^(1/2) - x

1. Domaine de définition

Dom f = [ 0, →

x |      0      1     
x^(1/2) - x | / 0 + 0 -

2. Limites et asymptotes

\!\(lim\+\(x →  0 \)\) f(x) =  0         
\!\(lim\+\(x →  ∞ \)\) f(x) =  -∞         

3. Etude de f'

f'(x) =  (1 - 2 x^(1/2))/(2 x^(1/2))

x |      0      1/4     
(1 - 2 x^(1/2))/(2 x^(1/2)) | / | + 0 -

        1   1 Max = ( - , -)         4   4

4. Etude de f\"

f\"(x) =  -1/(4 x^(3/2))

x |      0     
-1/(4 x^(3/2)) | / | -

5. Graphe de f

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Créé avec Mathematica  (Mai 31, 2006)
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