extreme f(x)=3x^4-12x^3-60x^2+4

Lösung

extrempunkte

f (x) = 3 x^{4} - 12 x^{3} - 60 x^{2} + 4

Minimum (- 2, - 92), Maximum (0, 4), Minimum (5, - 1121)

Schritte zur Lösung

f^{'} (x) = 12 x^{3} - 36 x^{2} - 120 x

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 0,

Absteigend

: 0 < x < 5,

Ansteigend

: 5 < x < \infty

Stecke

x = - 2

3 x^{4} - 12 x^{3} - 60 x^{2} + 4 : - 92

Minimum (- 2, - 92)

Stecke

x = 0

3 x^{4} - 12 x^{3} - 60 x^{2} + 4 : 4

Maximum (0, 4)

Stecke

x = 5

3 x^{4} - 12 x^{3} - 60 x^{2} + 4 : - 1121

Minimum (5, - 1121)

Minimum (- 2, - 92), Maximum (0, 4), Minimum (5, - 1121)

e x t re m e f (x) = 13 e^{- x}

e x t re m e f (x) = - x^{4} - 6 x

e x t re m e P (X, Y) = 36 X^{2} - 9 Y^{2}

e x t re m e f (x) = 9 x^{2} - 2

e x t re m e \frac{4}{x}