extreme f(x)=x^4-50x^2+6

Lösung

extrempunkte

f (x) = x^{4} - 50 x^{2} + 6

Minimum (- 5, - 619), Maximum (0, 6), Minimum (5, - 619)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 100 x

Intervalle finden:

Absteigend

: - \infty < x < - 5,

Ansteigend

: - 5 < x < 0,

Absteigend

: 0 < x < 5,

Ansteigend

: 5 < x < \infty

Stecke

x = - 5

x^{4} - 50 x^{2} + 6 : - 619

Minimum (- 5, - 619)

Stecke

x = 0

x^{4} - 50 x^{2} + 6 : 6

Maximum (0, 6)

Stecke

x = 5

x^{4} - 50 x^{2} + 6 : - 619

Minimum (5, - 619)

Minimum (- 5, - 619), Maximum (0, 6), Minimum (5, - 619)

e x t re m e f (x, y) = 4 (x - y) - x^{2} - y^{2}

e x t re m e f (x) = 3 x^{2} - 12 x + 5, 0 \leq x \leq 3

e x t re m e f (x) = x - sin (x), 0 \leq x \leq 2 π

e x t re m e y = x^{2} - 2 x - 8

e x t re m e f (x, y) = 5^{2} x^{4} + 5^{2} y^{4} - 4 x y + 14