Funktion & Ableitungen
f(x) = (x - 1)·√x = x^{3/2} - x^{1/2}
f'(x) = 3/2·x^{1/2} - 1/2·x^{- 1/2}
f''(x) = 3/4·x^{- 1/2} + 1/4·x^{- 3/2}
Symmetrie
Keine untersuchte Symmetrie
Verhalten an den Grenzen des Definitionsbereiches
f(0) = 0
LIM (x → ∞) (x - 1)·√x = ∞
Y-Achsenabschnitt f(0)
f(0) = 0
Nullstellen f(x) = 0
(x - 1)·√x = 0 --> x = 0 ∨ x = 1
Extrempunkte f'(x) = 0
3/2·x^{1/2} - 1/2·x^{- 1/2} = 0
3/2·x - 1/2 = 0 --> x = 1/3
f(1/3) = - 2/9·√3 = - 0.3849 --> TP(0.3333 | - 0.3849)
Wendepunkte f''(x) = 0
3/4·x^{- 1/2} + 1/4·x^{- 3/2} = 0
3/4·x + 1/4 = 0 --> x = - 1/3 [nicht in D]