extreme f(x)=2x^4-4x^2+6

Lösung

extrempunkte

f (x) = 2 x^{4} - 4 x^{2} + 6

Minimum (- 1, 4), Maximum (0, 6), Minimum (1, 4)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 0,

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 1

2 x^{4} - 4 x^{2} + 6 : 4

Minimum (- 1, 4)

Stecke

x = 0

2 x^{4} - 4 x^{2} + 6 : 6

Maximum (0, 6)

Stecke

x = 1

2 x^{4} - 4 x^{2} + 6 : 4

Minimum (1, 4)

Minimum (- 1, 4), Maximum (0, 6), Minimum (1, 4)

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

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

e x t re m e f (x, y) = 5 x y - 7 x^{2} - y^{2} + 3 x - 6 y + 2

e x t re m e f (x) = x^{3} - 12 x y + y^{3}

e x t re m e x^{2} + 10 x + 23