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Beliebt Funktionen >

extreme f(x)=(x^3)/3-10x^2+96x+100

Lösung

extrempunkte

f (x) = \frac{x ^{3}}{3} - 10 x^{2} + 96 x + 100

Lösung

Maximum (8, \frac{1196}{3}), Minimum (12, 388)

Schritte zur Lösung

f^{'} (x) = x^{2} - 20 x + 96

Intervalle finden:

Ansteigend

: - \infty < x < 8,

Absteigend

: 8 < x < 12,

Ansteigend

: 12 < x < \infty

Stecke

x = 8

in

\frac{x ^{3}}{3} - 10 x^{2} + 96 x + 100 : \frac{1196}{3}

Maximum (8, \frac{1196}{3})

Stecke

x = 12

in

\frac{x ^{3}}{3} - 10 x^{2} + 96 x + 100 : 388

Minimum (12, 388)

Maximum (8, \frac{1196}{3}), Minimum (12, 388)

Graph

Beliebte Beispiele

extreme f(x)=-x^3+9x^2+120x-200,x>= 5

e x t re m e f (x) = - x^{3} + 9 x^{2} + 120 x - 200, x \geq 5

extreme f(x)=x^{3/4}-2x^{3/4}

e x t re m e f (x) = x^{\frac{3}{4}} - 2 x^{\frac{3}{4}}

extreme f(x)=x^{2/3}(x-6)

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

extreme (16a^4+16a)/(a^2+1-a)

e x t re m e \frac{16 a ^{4} + 16 a}{a ^{2} + 1 - a}

extreme f(x)=-2x^2-5xy-6y^2+32x+63y+9

e x t re m e f (x) = - 2 x^{2} - 5 x y - 6 y^{2} + 32 x + 63 y + 9