extreme f(x)=x^3-x^2-8x+4

Lösung

extrempunkte

f (x) = x^{3} - x^{2} - 8 x + 4

Maximum (- \frac{4}{3}, \frac{284}{27}), Minimum (2, - 8)

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 + 4 : \frac{284}{27}

Maximum (- \frac{4}{3}, \frac{284}{27})

Stecke

x = 2

x^{3} - x^{2} - 8 x + 4 : - 8

Minimum (2, - 8)

Maximum (- \frac{4}{3}, \frac{284}{27}), Minimum (2, - 8)

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

e x t re m e f (x, y) = x^{3} + y^{3} - 24 x y

e x t re m e f (x) = \frac{8}{x} + 2 π x^{2}

e x t re m e f (x, y) = 400 - 9 x^{2} - 36 y^{2}

e x t re m e f (x, y) = \frac{1}{3} x^{3} - x