extreme f(x)=3x^4-54x^2+2

Lösung

extrempunkte

f (x) = 3 x^{4} - 54 x^{2} + 2

Minimum (- 3, - 241), Maximum (0, 2), Minimum (3, - 241)

Schritte zur Lösung

f^{'} (x) = 12 x^{3} - 108 x

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 0,

Absteigend

: 0 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 3

3 x^{4} - 54 x^{2} + 2 : - 241

Minimum (- 3, - 241)

Stecke

x = 0

3 x^{4} - 54 x^{2} + 2 : 2

Maximum (0, 2)

Stecke

x = 3

3 x^{4} - 54 x^{2} + 2 : - 241

Minimum (3, - 241)

Minimum (- 3, - 241), Maximum (0, 2), Minimum (3, - 241)

e x t re m e f (x) = \frac{lo g _{10} ( x )}{x}

e x t re m e P (x, y) = 3 x + 4 y

e x t re m e f (1) = x + 3

e x t re m e f (x) = 4 cos (3 x)

e x t re m e f (x) = 4 x^{5} - 3 x^{4} + x^{3} - 2 x^{2} + x - 1