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Beliebt Funktionen >

extreme f(x)=(x^4)/4+5/3 x^3-5x^2-50x+1

Lösung

extrempunkte

f (x) = \frac{x ^{4}}{4} + \frac{5}{3} x^{3} - 5 x^{2} - 50 x + 1

Lösung

Minimum (- 5, \frac{887}{12}), Maximum (- 10, - \frac{50 10}{3} + 5010 - 24), Minimum (10, \frac{50 10}{3} - 24 - 5010)

Schritte zur Lösung

f^{'} (x) = x^{3} + 5 x^{2} - 10 x - 50

Intervalle finden:

Absteigend

: - \infty < x < - 5,

Ansteigend

: - 5 < x < - 10,

Absteigend

: - 10 < x < 10,

Ansteigend

: 10 < x < \infty

Stecke

x = - 5

in

\frac{x ^{4}}{4} + \frac{5}{3} x^{3} - 5 x^{2} - 50 x + 1 : \frac{887}{12}

Minimum (- 5, \frac{887}{12})

Stecke

x = - 10

in

\frac{x ^{4}}{4} + \frac{5}{3} x^{3} - 5 x^{2} - 50 x + 1 : - \frac{50 10}{3} + 5010 - 24

Maximum (- 10, - \frac{50 10}{3} + 5010 - 24)

Stecke

x = 10

in

\frac{x ^{4}}{4} + \frac{5}{3} x^{3} - 5 x^{2} - 50 x + 1 : \frac{50 10}{3} - 24 - 5010

Minimum (10, \frac{50 10}{3} - 24 - 5010)

Minimum (- 5, \frac{887}{12}), Maximum (- 10, - \frac{50 10}{3} + 5010 - 24), Minimum (10, \frac{50 10}{3} - 24 - 5010)

Graph

Beliebte Beispiele

extreme f(x,y)= 1/2 x^2+y^3-xy

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

extreme f(x)=2x^2-8x+2(0.5)

e x t re m e f (x) = 2 x^{2} - 8 x + 2 (0.5)

extreme f(xy)=4-x^2-2y^2

e x t re m e f (x y) = 4 - x^{2} - 2 y^{2}

extreme f(x,y)=x^3-12x+y^2+6y+14

e x t re m e f (x, y) = x^{3} - 12 x + y^{2} + 6 y + 14

extreme (sqrt(x-5))/4

e x t re m e \frac{x - 5}{4}