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Beliebt Funktionen >

extreme f(x)=-(x+2)^5(x-4)^4

Lösung

extrempunkte

f (x) = - (x + 2)^{5} (x - 4)^{4}

Lösung

Sattel (- 2, 0), Minimum (\frac{4}{3}, - \frac{409600000}{19683}), Maximum (4, 0)

Schritte zur Lösung

f^{'} (x) = - 5 (x + 2)^{4} (x - 4)^{4} - 4 (x - 4)^{3} (x + 2)^{5}

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < \frac{4}{3},

Ansteigend

: \frac{4}{3} < x < 4,

Absteigend

: 4 < x < \infty

Stecke

x = - 2

in

- (x + 2)^{5} (x - 4)^{4} : 0

Sattel (- 2, 0)

Stecke

x = \frac{4}{3}

in

- (x + 2)^{5} (x - 4)^{4} : - \frac{409600000}{19683}

Minimum (\frac{4}{3}, - \frac{409600000}{19683})

Stecke

x = 4

in

- (x + 2)^{5} (x - 4)^{4} : 0

Maximum (4, 0)

Sattel (- 2, 0), Minimum (\frac{4}{3}, - \frac{409600000}{19683}), Maximum (4, 0)

Graph

Beliebte Beispiele

extreme f(x,y)=x^3-3x+xy^2

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\frac{d}{d x} (3 x o n [0.1])