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Beliebt Funktionen >

extreme x^3(x-1)^2(7x-4)

Lösung

extrempunkte

x^{3} (x - 1)^{2} (7 x - 4)

Lösung

Sattel (0, 0), Minimum (\frac{4 - 2}{7}, - \frac{368 2 - 44}{16807}), Maximum (\frac{4 + 2}{7}, \frac{368 2 + 44}{16807}), Minimum (1, 0)

Schritte zur Lösung

f^{'} (x) = 6 x^{2} (x - 1) (7 x^{2} - 8 x + 2)

Intervalle finden:

Absteigend

: - \infty < x < 0,

Absteigend

: 0 < x < \frac{4 - 2}{7},

Ansteigend

: \frac{4 - 2}{7} < x < \frac{4 + 2}{7},

Absteigend

: \frac{4 + 2}{7} < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = 0

in

x^{3} (x - 1)^{2} (7 x - 4) : 0

Sattel (0, 0)

Stecke

x = \frac{4 - 2}{7}

in

x^{3} (x - 1)^{2} (7 x - 4) : - \frac{368 2 - 44}{16807}

Minimum (\frac{4 - 2}{7}, - \frac{368 2 - 44}{16807})

Stecke

x = \frac{4 + 2}{7}

in

x^{3} (x - 1)^{2} (7 x - 4) : \frac{368 2 + 44}{16807}

Maximum (\frac{4 + 2}{7}, \frac{368 2 + 44}{16807})

Stecke

x = 1

in

x^{3} (x - 1)^{2} (7 x - 4) : 0

Minimum (1, 0)

Sattel (0, 0), Minimum (\frac{4 - 2}{7}, - \frac{368 2 - 44}{16807}), Maximum (\frac{4 + 2}{7}, \frac{368 2 + 44}{16807}), Minimum (1, 0)

Graph

Beliebte Beispiele

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

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