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

Lösung

extrempunkte

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

Minimum (- 2, - \frac{1}{3}), Maximum (0, 1)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 0,

Absteigend

: 0 < x < \infty

Stecke

x = - 2

\frac{x + 1}{x ^{2} + x + 1} : - \frac{1}{3}

Minimum (- 2, - \frac{1}{3})

Stecke

x = 0

\frac{x + 1}{x ^{2} + x + 1} : 1

Maximum (0, 1)

Minimum (- 2, - \frac{1}{3}), Maximum (0, 1)

e x t re m e f (x) = x, 0 \leq x \leq 16

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

e x t re m e f (x) = 2 x^{3} - 24 x^{2} + 72 x + 10

e x t re m e f (x) = x^{2} - 2 x, 0 \leq x \leq 4

e x t re m e f (x) = x^{3} - x^{2} - 8 x + 8, - 2 \leq x \leq 0