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

Lösung

extrempunkte

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

Minimum (0, 0), Maximum (2, - 4)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 1,

Ansteigend

: 1 < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = 0

\frac{x ^{2}}{1 - x} : 0

Minimum (0, 0)

Stecke

x = 2

\frac{x ^{2}}{1 - x} : - 4

Maximum (2, - 4)

Minimum (0, 0), Maximum (2, - 4)

e x t re m e f (x) = 4 - x^{2}, - 1 \leq x \leq 2

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

e x t re m e f (x) = \frac{x ^{3}}{3} - \frac{x ^{2}}{2} - 6 x + 4

e x t re m e \frac{x}{x ^{2} + 13 x + 36}

e x t re m e f (x) = 2 x^{3} - 12 x^{2} + 6