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Beliebt Funktionen >

extreme f(x)=-3x^4+4x^3+72x^2

Lösung

extrempunkte

f (x) = - 3 x^{4} + 4 x^{3} + 72 x^{2}

Lösung

Maximum (- 3, 297), Minimum (0, 0), Maximum (4, 640)

Schritte zur Lösung

f^{'} (x) = - 12 x^{3} + 12 x^{2} + 144 x

Intervalle finden:

Ansteigend

: - \infty < x < - 3,

Absteigend

: - 3 < x < 0,

Ansteigend

: 0 < x < 4,

Absteigend

: 4 < x < \infty

Stecke

x = - 3

in

- 3 x^{4} + 4 x^{3} + 72 x^{2} : 297

Maximum (- 3, 297)

Stecke

x = 0

in

- 3 x^{4} + 4 x^{3} + 72 x^{2} : 0

Minimum (0, 0)

Stecke

x = 4

in

- 3 x^{4} + 4 x^{3} + 72 x^{2} : 640

Maximum (4, 640)

Maximum (- 3, 297), Minimum (0, 0), Maximum (4, 640)

Graph

Beliebte Beispiele

extreme f(x)=(x-6)/(x^2-16),0<= x<4

e x t re m e f (x) = \frac{x - 6}{x ^{2} - 16}, 0 \leq x < 4

extreme x^2+2/x

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

extreme x^3-3/2 x^2,-1<= x<= 4

e x t re m e x^{3} - \frac{3}{2} x^{2}, - 1 \leq x \leq 4

extreme f(x)=x^3-6x^2+9x+7

e x t re m e f (x) = x^{3} - 6 x^{2} + 9 x + 7

extreme 1-2/(x^2+1)

e x t re m e 1 - \frac{2}{x ^{2} + 1}