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Beliebt Funktionen >

extreme f(x)=12x^5+45x^4-360x^3+6

Lösung

extrempunkte

f (x) = 12 x^{5} + 45 x^{4} - 360 x^{3} + 6

Lösung

Maximum (- 6, 42774), Sattel (0, 6), Minimum (3, - 3153)

Schritte zur Lösung

f^{'} (x) = 60 x^{4} + 180 x^{3} - 1080 x^{2}

Intervalle finden:

Ansteigend

: - \infty < x < - 6,

Absteigend

: - 6 < x < 0,

Absteigend

: 0 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 6

in

12 x^{5} + 45 x^{4} - 360 x^{3} + 6 : 42774

Maximum (- 6, 42774)

Stecke

x = 0

in

12 x^{5} + 45 x^{4} - 360 x^{3} + 6 : 6

Sattel (0, 6)

Stecke

x = 3

in

12 x^{5} + 45 x^{4} - 360 x^{3} + 6 : - 3153

Minimum (3, - 3153)

Maximum (- 6, 42774), Sattel (0, 6), Minimum (3, - 3153)

Graph

Beliebte Beispiele

extreme f(x)=(x^2+3x-1)^{1/3}

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

extreme f(x)=x^3-4x^2-x+1

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

extreme f(x,y)=(20000)/(3+x^2+y^2)

e x t re m e f (x, y) = \frac{20000}{3 + x ^{2} + y ^{2}}

extreme y= x/(x^2+64)

e x t re m e y = \frac{x}{x ^{2} + 64}

extreme f(x)=sqrt(-x^2+1),-1<= x<= 0

e x t re m e f (x) = - x^{2} + 1, - 1 \leq x \leq 0