extreme f(x)=x^3-x^2-8x+1

Lösung

extrempunkte

f (x) = x^{3} - x^{2} - 8 x + 1

Maximum (- \frac{4}{3}, \frac{203}{27}), Minimum (2, - 11)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 2 x - 8

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{4}{3},

Absteigend

: - \frac{4}{3} < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = - \frac{4}{3}

x^{3} - x^{2} - 8 x + 1 : \frac{203}{27}

Maximum (- \frac{4}{3}, \frac{203}{27})

Stecke

x = 2

x^{3} - x^{2} - 8 x + 1 : - 11

Minimum (2, - 11)

Maximum (- \frac{4}{3}, \frac{203}{27}), Minimum (2, - 11)

e x t re m e f (x) = (x + 1)^{\frac{2}{3}}

e x t re m e f (x) = x^{3} - x^{2} - 8 x - 2

e x t re m e f (y) = 7 x - x^{2} + 18

e x t re m e y = \frac{x ^{2} - 9}{x - 5}

e x t re m e 4 x^{3} - 210 x^{2} + 3600 x - 200