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Beliebt Funktionen >

extreme f(x)=2x^3-36x^2+162x-4

Lösung

extrempunkte

f (x) = 2 x^{3} - 36 x^{2} + 162 x - 4

Lösung

Maximum (3, 212), Minimum (9, - 4)

Schritte zur Lösung

f^{'} (x) = 6 x^{2} - 72 x + 162

Intervalle finden:

Ansteigend

: - \infty < x < 3,

Absteigend

: 3 < x < 9,

Ansteigend

: 9 < x < \infty

Stecke

x = 3

in

2 x^{3} - 36 x^{2} + 162 x - 4 : 212

Maximum (3, 212)

Stecke

x = 9

in

2 x^{3} - 36 x^{2} + 162 x - 4 : - 4

Minimum (9, - 4)

Maximum (3, 212), Minimum (9, - 4)

Graph

Beliebte Beispiele

extreme f(x)=20x(1-x)^3

e x t re m e f (x) = 20 x (1 - x)^{3}

extreme 4x^3-48x-1

e x t re m e 4 x^{3} - 48 x - 1

extreme f(x)= 1/2 x^4-4x^2+6

e x t re m e f (x) = \frac{1}{2} x^{4} - 4 x^{2} + 6

extreme f(x)=x^3-9x^2+15x+5

e x t re m e f (x) = x^{3} - 9 x^{2} + 15 x + 5

extreme f(x)=2x^2+(28)/x

e x t re m e f (x) = 2 x^{2} + \frac{28}{x}