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Beliebt Funktionen >

extreme-7(x+3)^2(x-1)(x-5)

Lösung

extrempunkte

- 7 (x + 3)^{2} (x - 1) (x - 5)

Lösung

Maximum (- 3, 0), Minimum (\frac{3 - 17}{2}, - \frac{175 ( 3 - 17 )}{2} - 26617 + 637), Maximum (\frac{3 + 17}{2}, - \frac{175 ( 3 + 17 )}{2} + 637 + 26617)

Schritte zur Lösung

f^{'} (x) = - 7 (4 x^{3} - 44 x - 24)

Intervalle finden:

Ansteigend

: - \infty < x < - 3,

Absteigend

: - 3 < x < \frac{3 - 17}{2},

Ansteigend

: \frac{3 - 17}{2} < x < \frac{3 + 17}{2},

Absteigend

: \frac{3 + 17}{2} < x < \infty

Stecke

x = - 3

in

- 7 (x + 3)^{2} (x - 1) (x - 5) : 0

Maximum (- 3, 0)

Stecke

x = \frac{3 - 17}{2}

in

- 7 (x + 3)^{2} (x - 1) (x - 5) : - \frac{175 ( 3 - 17 )}{2} - 26617 + 637

Minimum (\frac{3 - 17}{2}, - \frac{175 ( 3 - 17 )}{2} - 26617 + 637)

Stecke

x = \frac{3 + 17}{2}

in

- 7 (x + 3)^{2} (x - 1) (x - 5) : - \frac{175 ( 3 + 17 )}{2} + 637 + 26617

Maximum (\frac{3 + 17}{2}, - \frac{175 ( 3 + 17 )}{2} + 637 + 26617)

Maximum (- 3, 0), Minimum (\frac{3 - 17}{2}, - \frac{175 ( 3 - 17 )}{2} - 26617 + 637), Maximum (\frac{3 + 17}{2}, - \frac{175 ( 3 + 17 )}{2} + 637 + 26617)

Graph

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