extreme f(x)=x^4-30x^2+29

Lösung

extrempunkte

f (x) = x^{4} - 30 x^{2} + 29

Minimum (- 15, - 196), Maximum (0, 29), Minimum (15, - 196)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 60 x

Intervalle finden:

Absteigend

: - \infty < x < - 15,

Ansteigend

: - 15 < x < 0,

Absteigend

: 0 < x < 15,

Ansteigend

: 15 < x < \infty

Stecke

x = - 15

x^{4} - 30 x^{2} + 29 : - 196

Minimum (- 15, - 196)

Stecke

x = 0

x^{4} - 30 x^{2} + 29 : 29

Maximum (0, 29)

Stecke

x = 15

x^{4} - 30 x^{2} + 29 : - 196

Minimum (15, - 196)

Minimum (- 15, - 196), Maximum (0, 29), Minimum (15, - 196)

e x t re m e f (x, y) = e^{8 x} - x y^{3}

e x t re m e f (x y) = ln (4 - x - y)

e x t re m e f (x) = x^{4} - 6 x^{2} + 4

e x t re m e 4 x^{3} + 6 x + 2

e x t re m e f (x) = 5 x^{2} + 1, - 1 \leq x \leq 2