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Beliebt Funktionen >

extreme f(x)=x^4-2x^3-11x^2+12x+36

Lösung

extrempunkte

f (x) = x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 36

Lösung

Minimum (- 2, 0), Maximum (\frac{1}{2}, \frac{625}{16}), Minimum (3, 0)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 6 x^{2} - 22 x + 12

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < \frac{1}{2},

Absteigend

: \frac{1}{2} < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 2

in

x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 36 : 0

Minimum (- 2, 0)

Stecke

x = \frac{1}{2}

in

x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 36 : \frac{625}{16}

Maximum (\frac{1}{2}, \frac{625}{16})

Stecke

x = 3

in

x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 36 : 0

Minimum (3, 0)

Minimum (- 2, 0), Maximum (\frac{1}{2}, \frac{625}{16}), Minimum (3, 0)

Graph

Beliebte Beispiele

extreme y=9x^3-7

e x t re m e y = 9 x^{3} - 7

extreme x^3-12x^2+45x+8

e x t re m e x^{3} - 12 x^{2} + 45 x + 8

extreme |x^4-4x^2-2|,-2<= x<= 2

e x t re m e x^{4} - 4 x^{2} - 2, - 2 \leq x \leq 2

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

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

extreme f(x)=(8x)/(x^2+1)

e x t re m e f (x) = \frac{8 x}{x ^{2} + 1}