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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Sattel (0, 2), Maximum (4, \frac{778}{5}), Minimum (6, \frac{442}{5})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 4,

Absteigend

: 4 < x < 6,

Ansteigend

: 6 < x < \infty

Stecke

x = 0

in

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

Sattel (0, 2)

Stecke

x = 4

in

\frac{2}{5} x^{5} - 5 x^{4} + 16 x^{3} + 2 : \frac{778}{5}

Maximum (4, \frac{778}{5})

Stecke

x = 6

in

\frac{2}{5} x^{5} - 5 x^{4} + 16 x^{3} + 2 : \frac{442}{5}

Minimum (6, \frac{442}{5})

Sattel (0, 2), Maximum (4, \frac{778}{5}), Minimum (6, \frac{442}{5})

Graph

Beliebte Beispiele

extreme f(x)=x^3-5x^2+3x+12,-2<= x<= 4

e x t re m e f (x) = x^{3} - 5 x^{2} + 3 x + 12, - 2 \leq x \leq 4

extreme f(x)=x-sin(2x)

e x t re m e f (x) = x - sin (2 x)

extreme 110t^2e^{-1.2t}

e x t re m e 110 t^{2} e^{- 1.2 t}

extreme f(x)=-x^3+6x^2+x-1

e x t re m e f (x) = - x^{3} + 6 x^{2} + x - 1

extreme y=(x^3)/(x^2-4)

e x t re m e y = \frac{x ^{3}}{x ^{2} - 4}