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Beliebt Funktionen >

extreme f(x)=-(x+1)^2(x+3)^3(x-4)^2

Lösung

extrempunkte

f (x) = - (x + 1)^{2} \cdot (x + 3)^{3} \cdot (x - 4)^{2}

Lösung

Sattel (- 3, 0), Minimum (\frac{3 - 849}{14}, - \frac{6356351448 - 262734936 849}{3294172} - 432), Maximum (- 1, 0), Minimum (\frac{3 + 849}{14}, - \frac{6356351448 + 262734936 849}{3294172} - 432), Maximum (4, 0)

Schritte zur Lösung

f^{'} (x) = - 2 x (x + 3)^{3} (x - 4)^{2} - 2 (x + 3)^{3} (x - 4)^{2} - 5 x^{6} - 14 x^{5} + 74 x^{4} + 260 x^{3} + 51 x^{2} - 342 x - 216

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Absteigend

: - 3 < x < \frac{3 - 849}{14},

Ansteigend

: \frac{3 - 849}{14} < x < - 1,

Absteigend

: - 1 < x < \frac{3 + 849}{14},

Ansteigend

: \frac{3 + 849}{14} < x < 4,

Absteigend

: 4 < x < \infty

Stecke

x = - 3

in

- (x + 1)^{2} \cdot (x + 3)^{3} \cdot (x - 4)^{2} : 0

Sattel (- 3, 0)

Stecke

x = \frac{3 - 849}{14}

in

- (x + 1)^{2} \cdot (x + 3)^{3} \cdot (x - 4)^{2} : - \frac{6356351448 - 262734936 849}{3294172} - 432

Minimum (\frac{3 - 849}{14}, - \frac{6356351448 - 262734936 849}{3294172} - 432)

Stecke

x = - 1

in

- (x + 1)^{2} \cdot (x + 3)^{3} \cdot (x - 4)^{2} : 0

Maximum (- 1, 0)

Stecke

x = \frac{3 + 849}{14}

in

- (x + 1)^{2} \cdot (x + 3)^{3} \cdot (x - 4)^{2} : - \frac{6356351448 + 262734936 849}{3294172} - 432

Minimum (\frac{3 + 849}{14}, - \frac{6356351448 + 262734936 849}{3294172} - 432)

Stecke

x = 4

in

- (x + 1)^{2} \cdot (x + 3)^{3} \cdot (x - 4)^{2} : 0

Maximum (4, 0)

Sattel (- 3, 0), Minimum (\frac{3 - 849}{14}, - \frac{6356351448 - 262734936 849}{3294172} - 432), Maximum (- 1, 0), Minimum (\frac{3 + 849}{14}, - \frac{6356351448 + 262734936 849}{3294172} - 432), Maximum (4, 0)

Graph

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