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Beliebt Funktionen >

extreme x^4(x-2)(x+3)

Lösung

extrempunkte

x^{4} (x - 2) (x + 3)

Lösung

Minimum (\frac{- 5 - 601}{12}, \frac{- 149737888 - 4634912 601}{2985984}), Maximum (0, 0), Minimum (\frac{- 5 + 601}{12}, \frac{4634912 601 - 149737888}{2985984})

Schritte zur Lösung

f^{'} (x) = x^{3} (6 x^{2} + 5 x - 24)

Intervalle finden:

Absteigend

: - \infty < x < \frac{- 5 - 601}{12},

Ansteigend

: \frac{- 5 - 601}{12} < x < 0,

Absteigend

: 0 < x < \frac{601 - 5}{12},

Ansteigend

: \frac{601 - 5}{12} < x < \infty

Stecke

x = \frac{- 5 - 601}{12}

in

x^{4} (x - 2) (x + 3) : \frac{- 149737888 - 4634912 601}{2985984}

Minimum (\frac{- 5 - 601}{12}, \frac{- 149737888 - 4634912 601}{2985984})

Stecke

x = 0

in

x^{4} (x - 2) (x + 3) : 0

Maximum (0, 0)

Stecke

x = \frac{- 5 + 601}{12}

in

x^{4} (x - 2) (x + 3) : \frac{4634912 601 - 149737888}{2985984}

Minimum (\frac{- 5 + 601}{12}, \frac{4634912 601 - 149737888}{2985984})

Minimum (\frac{- 5 - 601}{12}, \frac{- 149737888 - 4634912 601}{2985984}), Maximum (0, 0), Minimum (\frac{- 5 + 601}{12}, \frac{4634912 601 - 149737888}{2985984})

Graph

Beliebte Beispiele

slopeintercept (5x-y)/3 =(5x-4)/6

s l o p e in t erce pt \frac{5 x - y}{3} = \frac{5 x - 4}{6}

invers f(x)=4n+16

in v erse f (x) = 4 n + 16

f(x)=(3\sqrt[3]{x}+4)^2

f (x) = (3 3 x + 4)^{2}

vereinfachen (2.7)(10.16)

s im pl i f y (2.7) (10.16)

in v erse - x