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Beliebt Funktionen >

extreme f(x)=x^4-5x^3+x^2+21x-18

Lösung

extrempunkte

f (x) = x^{4} - 5 x^{3} + x^{2} + 21 x - 18

Lösung

Minimum (- 1, - 32), Maximum (\frac{7}{4}, \frac{1125}{256}), Minimum (3, 0)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 15 x^{2} + 2 x + 21

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < \frac{7}{4},

Absteigend

: \frac{7}{4} < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 1

in

x^{4} - 5 x^{3} + x^{2} + 21 x - 18 : - 32

Minimum (- 1, - 32)

Stecke

x = \frac{7}{4}

in

x^{4} - 5 x^{3} + x^{2} + 21 x - 18 : \frac{1125}{256}

Maximum (\frac{7}{4}, \frac{1125}{256})

Stecke

x = 3

in

x^{4} - 5 x^{3} + x^{2} + 21 x - 18 : 0

Minimum (3, 0)

Minimum (- 1, - 32), Maximum (\frac{7}{4}, \frac{1125}{256}), Minimum (3, 0)

Graph

Beliebte Beispiele

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

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

extreme 1/(sqrt(3-2x-x^2))

e x t re m e \frac{1}{3 - 2 x - x ^{2}}

extreme f(x)=xsqrt(x^2+36)

e x t re m e f (x) = x x^{2} + 36

extreme (-2x)/(x^2+y^2+1)

e x t re m e \frac{- 2 x}{x ^{2} + y ^{2} + 1}

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

e x t re m e y = (x - 4)^{2} (x + 2)^{3}