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Beliebt Funktionen >

extreme f(x)=(x+1)^2(x-4)^5(x-7)^4

Lösung

extrempunkte

f (x) = (x + 1)^{2} (x - 4)^{5} (x - 7)^{4}

Lösung

Maximum (- 1, 0), Minimum (\frac{32 - 969}{11}, \frac{- 5.99965 E 14 969 - 1.74164 E 16}{285311670611} - \frac{1024 ( 538920 969 - 18340105 )}{14641} - 2458624), Sattel (4, 0), Maximum (\frac{32 + 969}{11}, \frac{5.99965 E 14 969 - 1.74164 E 16}{285311670611} - \frac{1024 ( - 18340105 - 538920 969 )}{14641} - 2458624), Minimum (7, 0)

Schritte zur Lösung

f^{'} (x) = (x - 4)^{4} (x - 7)^{3} (x + 1) (11 x^{2} - 64 x + 5)

Intervalle finden:

Ansteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < \frac{32 - 969}{11},

Ansteigend

: \frac{32 - 969}{11} < x < 4,

Ansteigend

: 4 < x < \frac{32 + 969}{11},

Absteigend

: \frac{32 + 969}{11} < x < 7,

Ansteigend

: 7 < x < \infty

Stecke

x = - 1

in

(x + 1)^{2} (x - 4)^{5} (x - 7)^{4} : 0

Maximum (- 1, 0)

Stecke

x = \frac{32 - 969}{11}

in

(x + 1)^{2} (x - 4)^{5} (x - 7)^{4} : \frac{- 5.99965 E 14 969 - 1.74164 E 16}{285311670611} - \frac{1024 ( 538920 969 - 18340105 )}{14641} - 2458624

Minimum (\frac{32 - 969}{11}, \frac{- 5.99965 E 14 969 - 1.74164 E 16}{285311670611} - \frac{1024 ( 538920 969 - 18340105 )}{14641} - 2458624)

Stecke

x = 4

in

(x + 1)^{2} (x - 4)^{5} (x - 7)^{4} : 0

Sattel (4, 0)

Stecke

x = \frac{32 + 969}{11}

in

(x + 1)^{2} (x - 4)^{5} (x - 7)^{4} : \frac{5.99965 E 14 969 - 1.74164 E 16}{285311670611} - \frac{1024 ( - 18340105 - 538920 969 )}{14641} - 2458624

Maximum (\frac{32 + 969}{11}, \frac{5.99965 E 14 969 - 1.74164 E 16}{285311670611} - \frac{1024 ( - 18340105 - 538920 969 )}{14641} - 2458624)

Stecke

x = 7

in

(x + 1)^{2} (x - 4)^{5} (x - 7)^{4} : 0

Minimum (7, 0)

Maximum (- 1, 0), Minimum (\frac{32 - 969}{11}, \frac{- 5.99965 E 14 969 - 1.74164 E 16}{285311670611} - \frac{1024 ( 538920 969 - 18340105 )}{14641} - 2458624), Sattel (4, 0), Maximum (\frac{32 + 969}{11}, \frac{5.99965 E 14 969 - 1.74164 E 16}{285311670611} - \frac{1024 ( - 18340105 - 538920 969 )}{14641} - 2458624), Minimum (7, 0)

Graph

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