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Beliebt Funktionen >

extreme f(x)=(x^3)/3-5x^2+16x-100

Lösung

extrempunkte

f (x) = \frac{x ^{3}}{3} - 5 x^{2} + 16 x - 100

Lösung

Maximum (2, - \frac{256}{3}), Minimum (8, - \frac{364}{3})

Schritte zur Lösung

f^{'} (x) = x^{2} - 10 x + 16

Intervalle finden:

Ansteigend

: - \infty < x < 2,

Absteigend

: 2 < x < 8,

Ansteigend

: 8 < x < \infty

Stecke

x = 2

in

\frac{x ^{3}}{3} - 5 x^{2} + 16 x - 100 : - \frac{256}{3}

Maximum (2, - \frac{256}{3})

Stecke

x = 8

in

\frac{x ^{3}}{3} - 5 x^{2} + 16 x - 100 : - \frac{364}{3}

Minimum (8, - \frac{364}{3})

Maximum (2, - \frac{256}{3}), Minimum (8, - \frac{364}{3})

Graph

Beliebte Beispiele

extreme f(x)=x^3+10x^2+8

e x t re m e f (x) = x^{3} + 10 x^{2} + 8

extreme f(x,y)=-6x^2+5xy-y^2+x+y

e x t re m e f (x, y) = - 6 x^{2} + 5 x y - y^{2} + x + y

extreme f(x,y)=3x^2y-y^2+5xy^2

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

extreme f(x)=2x+cos(x)

e x t re m e f (x) = 2 x + cos (x)

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

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