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Beliebt Funktionen >

extreme f(x)= 3/4 x^4+15x^3+75x^2-23

Lösung

extrempunkte

f (x) = \frac{3}{4} x^{4} + 15 x^{3} + 75 x^{2} - 23

Lösung

Minimum (- 10, - 23), Maximum (- 5, \frac{1783}{4}), Minimum (0, - 23)

Schritte zur Lösung

f^{'} (x) = 3 x^{3} + 45 x^{2} + 150 x

Intervalle finden:

Absteigend

: - \infty < x < - 10,

Ansteigend

: - 10 < x < - 5,

Absteigend

: - 5 < x < 0,

Ansteigend

: 0 < x < \infty

Stecke

x = - 10

in

\frac{3}{4} x^{4} + 15 x^{3} + 75 x^{2} - 23 : - 23

Minimum (- 10, - 23)

Stecke

x = - 5

in

\frac{3}{4} x^{4} + 15 x^{3} + 75 x^{2} - 23 : \frac{1783}{4}

Maximum (- 5, \frac{1783}{4})

Stecke

x = 0

in

\frac{3}{4} x^{4} + 15 x^{3} + 75 x^{2} - 23 : - 23

Minimum (0, - 23)

Minimum (- 10, - 23), Maximum (- 5, \frac{1783}{4}), Minimum (0, - 23)

Graph

Beliebte Beispiele

extreme f(x)=x^3-(3/2)x^2

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

extreme f(x)=x^2,-1<= x<= 2

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

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

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

extreme f(x)= 1/2 x-sin(x)

e x t re m e f (x) = \frac{1}{2} x - sin (x)

extreme f(x)=xe^{3-(x/4)}

e x t re m e f (x) = x e^{3 - (\frac{x}{4})}