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Beliebt Funktionen >

extreme f(x)= 4/3 x^3-25/2 x^2+6x+4

Lösung

extrempunkte

f (x) = \frac{4}{3} x^{3} - \frac{25}{2} x^{2} + 6 x + 4

Lösung

Maximum (\frac{1}{4}, \frac{455}{96}), Minimum (6, - 122)

Schritte zur Lösung

f^{'} (x) = 4 x^{2} - 25 x + 6

Intervalle finden:

Ansteigend

: - \infty < x < \frac{1}{4},

Absteigend

: \frac{1}{4} < x < 6,

Ansteigend

: 6 < x < \infty

Stecke

x = \frac{1}{4}

in

\frac{4}{3} x^{3} - \frac{25}{2} x^{2} + 6 x + 4 : \frac{455}{96}

Maximum (\frac{1}{4}, \frac{455}{96})

Stecke

x = 6

in

\frac{4}{3} x^{3} - \frac{25}{2} x^{2} + 6 x + 4 : - 122

Minimum (6, - 122)

Maximum (\frac{1}{4}, \frac{455}{96}), Minimum (6, - 122)

Graph

Beliebte Beispiele

extreme f(xy)=x^2y-15xy^2+12y

e x t re m e f (x y) = x^{2} y - 15 x y^{2} + 12 y

extreme f(x)=12x^2-18x

e x t re m e f (x) = 12 x^{2} - 18 x

extreme-6x^5+180x^3-1350x+14

e x t re m e - 6 x^{5} + 180 x^{3} - 1350 x + 14

extreme ln(1-3x)

e x t re m e ln (1 - 3 x)

extreme ln(3x^2+12)

e x t re m e ln (3 x^{2} + 12)