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Beliebt Funktionen >

extreme f(x)=((x-1)^2)/(x-3)

Lösung

extrempunkte

f (x) = \frac{( x - 1 ) ^{2}}{x - 3}

Lösung

Maximum (1, 0), Minimum (5, 8)

Schritte zur Lösung

f^{'} (x) = \frac{x ^{2} - 6 x + 5}{( x - 3 ) ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < 1,

Absteigend

: 1 < x < 3,

Absteigend

: 3 < x < 5,

Ansteigend

: 5 < x < \infty

Stecke

x = 1

in

\frac{( x - 1 ) ^{2}}{x - 3} : 0

Maximum (1, 0)

Stecke

x = 5

in

\frac{( x - 1 ) ^{2}}{x - 3} : 8

Minimum (5, 8)

Maximum (1, 0), Minimum (5, 8)

Graph

Beliebte Beispiele

extreme f(x)=3x^2+(48)/(x^2)

e x t re m e f (x) = 3 x^{2} + \frac{48}{x ^{2}}

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

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

extreme f(x)=2xy-15y^2

e x t re m e f (x) = 2 x y - 15 y^{2}

extreme f(x)=6sin(x)+cot(x)

e x t re m e f (x) = 6 sin (x) + cot (x)

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

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