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

Lösung

extrempunkte

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

Minimum (- 4, - \frac{2}{27}), Maximum (0, 0)

Schritte zur Lösung

f^{'} (x) = \frac{x ( - x - 4 )}{( x - 2 ) ^{4}}

Intervalle finden:

Absteigend

: - \infty < x < - 4,

Ansteigend

: - 4 < x < 0,

Absteigend

: 0 < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = - 4

\frac{x ^{2}}{( x - 2 ) ^{3}} : - \frac{2}{27}

Minimum (- 4, - \frac{2}{27})

Stecke

x = 0

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

Maximum (0, 0)

Minimum (- 4, - \frac{2}{27}), Maximum (0, 0)

r an g e \frac{x}{x ^{2} - 6 x + 8}

e x t re m e f (x) = \frac{( 3 x - 1 )}{( 8 x - 3 )}

mi d p o in t (- 2, 3), (4, - 1)

m o n o t o n e f (x) = {x ∣ x < 6}

d o main f (x) = (x + 1)^{2} - 4