extreme (2x-2)/(x^2+x)+1

Lösung

extrempunkte

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

Minimum (1 - 2, 2 (3 + 22) + 1), Maximum (1 + 2, 2 (3 - 22) + 1)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < 1 - 2,

Ansteigend

: 1 - 2 < x < 0,

Ansteigend

: 0 < x < 1 + 2,

Absteigend

: 1 + 2 < x < \infty

Stecke

x = 1 - 2

\frac{2 x - 2}{x ^{2} + x} + 1 : 2 (3 + 22) + 1

Minimum (1 - 2, 2 (3 + 22) + 1)

Stecke

x = 1 + 2

\frac{2 x - 2}{x ^{2} + x} + 1 : 2 (3 - 22) + 1

Maximum (1 + 2, 2 (3 - 22) + 1)

Minimum (1 - 2, 2 (3 + 22) + 1), Maximum (1 + 2, 2 (3 - 22) + 1)

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e x t re m e 6 sinh (3 x) cosh (3 x)