extreme f(x)=x^4-98x^2+4

Lösung

extrempunkte

f (x) = x^{4} - 98 x^{2} + 4

Minimum (- 7, - 2397), Maximum (0, 4), Minimum (7, - 2397)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 196 x

Intervalle finden:

Absteigend

: - \infty < x < - 7,

Ansteigend

: - 7 < x < 0,

Absteigend

: 0 < x < 7,

Ansteigend

: 7 < x < \infty

Stecke

x = - 7

x^{4} - 98 x^{2} + 4 : - 2397

Minimum (- 7, - 2397)

Stecke

x = 0

x^{4} - 98 x^{2} + 4 : 4

Maximum (0, 4)

Stecke

x = 7

x^{4} - 98 x^{2} + 4 : - 2397

Minimum (7, - 2397)

Minimum (- 7, - 2397), Maximum (0, 4), Minimum (7, - 2397)

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

e x t re m e f (x) = (x + 2)^{3} - 5

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

e x t re m e f (x) = 6 x^{\frac{2}{3}}

e x t re m e 2 x^{3} + 3 x^{2} - 72 x