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Beliebt Funktionen >

extreme f(x)= 2/5 x^5+5x^4+16x^3-15

Lösung

extrempunkte

f (x) = \frac{2}{5} x^{5} + 5 x^{4} + 16 x^{3} - 15

Lösung

Maximum (- 6, - \frac{507}{5}), Minimum (- 4, - \frac{843}{5}), Sattel (0, - 15)

Schritte zur Lösung

f^{'} (x) = 2 x^{4} + 20 x^{3} + 48 x^{2}

Intervalle finden:

Ansteigend

: - \infty < x < - 6,

Absteigend

: - 6 < x < - 4,

Ansteigend

: - 4 < x < 0,

Ansteigend

: 0 < x < \infty

Stecke

x = - 6

in

\frac{2}{5} x^{5} + 5 x^{4} + 16 x^{3} - 15 : - \frac{507}{5}

Maximum (- 6, - \frac{507}{5})

Stecke

x = - 4

in

\frac{2}{5} x^{5} + 5 x^{4} + 16 x^{3} - 15 : - \frac{843}{5}

Minimum (- 4, - \frac{843}{5})

Stecke

x = 0

in

\frac{2}{5} x^{5} + 5 x^{4} + 16 x^{3} - 15 : - 15

Sattel (0, - 15)

Maximum (- 6, - \frac{507}{5}), Minimum (- 4, - \frac{843}{5}), Sattel (0, - 15)

Graph

Beliebte Beispiele

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

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

f (t) = 2 x

extreme T(x,y)=(x+3y,-x+5y)

e x t re m e T (x, y) = (x + 3 y, - x + 5 y)

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

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

extreme f(x,y)=8x^3+y^3+6xy

e x t re m e f (x, y) = 8 x^{3} + y^{3} + 6 x y