extreme f(x)=x^4-7x^3-13x^2

Lösung

extrempunkte

f (x) = x^{4} - 7 x^{3} - 13 x^{2}

Minimum (\frac{21 - 857}{8}, \frac{5999 857 - 178187}{512}), Maximum (0, 0), Minimum (\frac{21 + 857}{8}, - \frac{178187 + 5999 857}{512})

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 21 x^{2} - 26 x

Intervalle finden:

Absteigend

: - \infty < x < \frac{21 - 857}{8},

Ansteigend

: \frac{21 - 857}{8} < x < 0,

Absteigend

: 0 < x < \frac{21 + 857}{8},

Ansteigend

: \frac{21 + 857}{8} < x < \infty

Stecke

x = \frac{21 - 857}{8}

x^{4} - 7 x^{3} - 13 x^{2} : \frac{5999 857 - 178187}{512}

Minimum (\frac{21 - 857}{8}, \frac{5999 857 - 178187}{512})

Stecke

x = 0

x^{4} - 7 x^{3} - 13 x^{2} : 0

Maximum (0, 0)

Stecke

x = \frac{21 + 857}{8}

x^{4} - 7 x^{3} - 13 x^{2} : - \frac{178187 + 5999 857}{512}

Minimum (\frac{21 + 857}{8}, - \frac{178187 + 5999 857}{512})

Minimum (\frac{21 - 857}{8}, \frac{5999 857 - 178187}{512}), Maximum (0, 0), Minimum (\frac{21 + 857}{8}, - \frac{178187 + 5999 857}{512})

g l o ba l f (x) = - x^{2} + 11

in v erse f (x) = (x - 8)^{7}

e x t re m e f (x) = (4 - 3 x)^{2}

in f l ec t i o n f (x) = 5 x^{3} - 3 x

d o main g (t) = \frac{3}{t}